CAPRI Online Manual (update)

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<o:Author>Sebastian Neuenfeldt</o:Author>
<o:LastAuthor>Alexander Gocht</o:LastAuthor>
<o:Revision>2</o:Revision>
<o:LastPrinted>2014-06-13T10:46:00Z</o:LastPrinted>
<o:Created>2019-10-11T11:19:00Z</o:Created>
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<o:Company>Microsoft</o:Company>
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<h1 style='text-align:justify'><!–[if supportFields]> MACROBUTTON MTEditEquationSection2 Formel-Kapitel 1 Abschnitt 1 SEQ MTEqn \r \h \* MERGEFORMAT SEQ MTSec \r 1 \h \* MERGEFORMAT SEQ MTChap \r 1 \h \* MERGEFORMAT <![endif]–><!–[if supportFields]><![endif]–>The Use of Mathematical Programming in Agriculture – Generating more economic sophisticated solutions<a style='mso-footnote-id:ftn1' href=“#_ftn1” name=“_ftnref1” title=“”><![if !supportFootnotes]><span lang=EN-GB style='font-size:14.0pt;line-height:115%;font-family:“Cambria”,serif; mso-ascii-theme-font:major-latin;mso-fareast-font-family:“Times New Roman”; mso-fareast-theme-font:major-fareast;mso-hansi-theme-font:major-latin; mso-bidi-font-family:“Times New Roman”;mso-bidi-theme-font:major-bidi; color:#365F91;mso-themecolor:accent1;mso-themeshade:191;mso-ansi-language:EN-GB; mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>[1]<![endif]></a><o:p></o:p></h1>

<h2 style='text-align:justify'>Reading guide as training material<a style='mso-footnote-id:ftn2' href=“#_ftn2” name=“_ftnref2” title=“”><![if !supportFootnotes]><span lang=EN-GB style='font-size:13.0pt;line-height:115%;font-family:“Cambria”,serif; mso-ascii-theme-font:major-latin;mso-fareast-font-family:“Times New Roman”; mso-fareast-theme-font:major-fareast;mso-hansi-theme-font:major-latin; mso-bidi-font-family:“Times New Roman”;mso-bidi-theme-font:major-bidi; color:#4F81BD;mso-themecolor:accent1;mso-ansi-language:EN-GB;mso-fareast-language: EN-US;mso-bidi-language:AR-SA'>[2]<![endif]></a><o:p></o:p></h2>

This reading material should guide you theoretically through the derivation of parameter calibration of PMP terms for economically more sophisticated programming models. In this guide you should understand how a linear programming works and what the shortcomings are, how positive mathematical programming models are calibrated and how these different models behave if input parameters change.<o:p></o:p>

Additionally there is a hands on excel (Session_B5_Beginners_Advanced_PMP_example.xlsx) and GAMS file (Session_B5_Advanced_PMP_example.gms) for the beginners and advanced, respectively.<a style='mso-footnote-id:ftn3' href=“#_ftn3” name=“_ftnref3” title=“”><![if !supportFootnotes]><span lang=EN-GB style='font-size:11.0pt;line-height:115%;font-family:“Calibri”,sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:“Times New Roman”; mso-bidi-theme-font:minor-bidi;mso-ansi-language:EN-GB;mso-fareast-language: EN-US;mso-bidi-language:AR-SA'>[3]<![endif]></a> With the examples provided in the files you can train how to set up and solve a linear programming model, calibrate the positive mathematical programming models and simulate the price changes. You are free to also define other price changes once you are familiar with the price scenarios given here in the guide.<o:p></o:p>

<h2 style='text-align:justify'>Introduction<o:p></o:p></h2>

The use of mathematical programming models is strongly related to the decision making situation of a farmer. Farmers must make decisions about the production plan. The decisions are not independent from physical or financial constraints. Traditionally, farmers relied on intuition, experience or their neighbour’s actions. Using formal methods like mathematical programming models can enhance the farmers profits, at least when the production program becomes more complex. Those mathematical programming models predict quite accurately the behaviour of a representative farmer. This predictive “power” makes those representative farm models useful for policy analysis (Hazell & Norton, 1986).<o:p></o:p>

<h2 style='text-align:justify'>A linear programming model <o:p></o:p></h2>

A linear programming model is a method to find the profit maximizing combination of production activities which is feasible subject to a set of farm constraints. A linear programming model requires some information about: <o:p></o:p>

<![if !supportLists]>-          <![endif]>the alternative production activities, their unit of measurement, their resource requirements and any production constraints<o:p></o:p>

<![if !supportLists]>-          <![endif]>the fixed resource constraints<o:p></o:p>

<![if !supportLists]>-          <![endif]>gross margins of the production activities<o:p></o:p>

In the following a simple linear programming model for a farm is presented (Hazell & Norton, 1986). <o:p></o:p>

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<!–[if supportFields]> MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTSec \c \* Arabic \* MERGEFORMAT 1. SEQ MTEqn \c \* Arabic \* MERGEFORMAT 3)<![endif]–><![if !supportNestedAnchors]><a name=ZEqnNum950209></a><![endif]><!–[if supportFields]><![endif]–> <v:shape id=“_x0000_i1027” type=“#_x0000_t75” style='width:75pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image003.wmz”

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</o:OLEObject> </xml><![endif]–>

Where:<o:p></o:p>

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o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1028”

DrawAspect="Content" ObjectID="_1632305214">

</o:OLEObject> </xml><![endif]–> is the level of <v:shape id=“_x0000_i1029” type=“#_x0000_t75” style='width:6.75pt;height:15pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image005.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1029”

DrawAspect="Content" ObjectID="_1632305215">

</o:OLEObject> </xml><![endif]–>-th production activity<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1030” type=“#_x0000_t75” style='width:9pt;height:9.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image006.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1030”

DrawAspect="Content" ObjectID="_1632305216">

</o:OLEObject> </xml><![endif]–> the number of production activities<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1031” type=“#_x0000_t75” style='width:9.75pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image007.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1031”

DrawAspect="Content" ObjectID="_1632305217">

</o:OLEObject> </xml><![endif]–> the gross margin of production activity <v:shape id=“_x0000_i1032” type=“#_x0000_t75” style='width:6.75pt; height:15pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image008.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1032”

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</o:OLEObject> </xml><![endif]–> <o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1033” type=“#_x0000_t75” style='width:13.5pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image009.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1033”

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</o:OLEObject> </xml><![endif]–> the quantity of the <v:shape id=“_x0000_i1034” type=“#_x0000_t75” style='width:6pt;height:12pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image010.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1034”

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</o:OLEObject> </xml><![endif]–>-th resource requirement (<v:shape id=“_x0000_i1035” type=“#_x0000_t75” style='width:40.5pt;height:13.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image011.wmz”

o:title=""/>

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</o:OLEObject> </xml><![endif]–>) to produce one unit of <v:shape id=“_x0000_i1036” type=“#_x0000_t75” style='width:6.75pt;height:15pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image012.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1036”

DrawAspect="Content" ObjectID="_1632305222">

</o:OLEObject> </xml><![endif]–>-th production activity<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1037” type=“#_x0000_t75” style='width:12pt;height:9.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image013.wmz”

o:title=""/>

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DrawAspect="Content" ObjectID="_1632305223">

</o:OLEObject> </xml><![endif]–> is the number of resources<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1038” type=“#_x0000_t75” style='width:9.75pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image014.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1038”

DrawAspect="Content" ObjectID="_1632305224">

</o:OLEObject> </xml><![endif]–> the amount of the <v:shape id=“_x0000_i1039” type=“#_x0000_t75” style='width:6pt;height:12pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image015.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1039”

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</o:OLEObject> </xml><![endif]–>-th resource available<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1040” type=“#_x0000_t75” style='width:9.75pt;height:12.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image016.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1040”

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</o:OLEObject> </xml><![endif]–> are the dual variables associated with the resource constraints<o:p></o:p>

The problem is to find the amount of production activity levels that maximize the total gross margin (<v:shape id=“_x0000_i1041” type=“#_x0000_t75” style='width:9pt;height:11.25pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image017.wmz”

o:title=""/>

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</o:OLEObject> </xml><![endif]–>) that does not violate the constraints or contain negative activity levels. The dual variables of the resource constraints (<v:shape id=“_x0000_i1042” type=“#_x0000_t75” style='width:9.75pt;height:12.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image016.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1042”

DrawAspect="Content" ObjectID="_1632305228">

</o:OLEObject> </xml><![endif]–>) are also called shadow prices of the resources. Those values give the maximum value a representative farmer is willing to pay to enhance the resource constraints. For instance, the shadow price of land is the maximum value of one additional unit of land to increase the most profitable production activity.<o:p></o:p>

For the linear programming model a few assumptions are made. At first, an optimization problem is faced, that means, that the objective function <!–[if supportFields]> GOTOBUTTON ZEqnNum225900 \* MERGEFORMAT REF ZEqnNum225900 \* Charformat \! \* MERGEFORMAT (1.1)<![endif]–><!–[if supportFields]><![endif]–> is either maximized or minimized. It is important to have at least one nonzero constraint <!–[if supportFields]> GOTOBUTTON ZEqnNum136343 \* MERGEFORMAT REF ZEqnNum136343 \* Charformat \! \* MERGEFORMAT (1.2)<![endif]–><!–[if supportFields]><![endif]–> and that there is only a finite number of production activities <!–[if supportFields]> GOTOBUTTON ZEqnNum950209 \* MERGEFORMAT REF ZEqnNum950209 \* Charformat \! \* MERGEFORMAT (1.3)<![endif]–><!–[if supportFields]><![endif]–> and constraints so that a solution can be find. The model coefficients – gross margins <v:shape id=“_x0000_i1043” type=“#_x0000_t75” style='width:9.75pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image018.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1043”

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</o:OLEObject> </xml><![endif]–>, resource requirements <v:shape id=“_x0000_i1044” type=“#_x0000_t75” style='width:13.5pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image019.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1044”

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</o:OLEObject> </xml><![endif]–> and amounts of resource available <v:shape id=“_x0000_i1045” type=“#_x0000_t75” style='width:9.75pt; height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image020.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1045”

DrawAspect="Content" ObjectID="_1632305231">

</o:OLEObject> </xml><![endif]–> – are assumed to be known and constant. This also leads to the fact, that the increase of total expected gross margin and the resource requirements per unit are proportional to the used production activity level and hence, independent of the activity level used. Further it is assumed, that the resources can be used and the activities produced in quantities are fractional units. The units of the resources or activities are identical. No interaction effects between the production activities are allowed, which means, that the total product is the sum of their individual products. <o:p></o:p>

<h3 style='text-align:justify'>A small example<o:p></o:p></h3>

We start with a small example of a linear programming model to become familiar with mathematical programming models.<o:p></o:p>

<a name=“_Ref389667383”>Table </a><!–[if supportFields]> SEQ Table \* ARABIC <![endif]–>1<!–[if supportFields]><![endif]–>. Programming tableau with objective function and constraints (Excel file sheet “Simple LP”, GAMS file model “LP”)<o:p></o:p>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
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<td width=278 nowrap colspan=4 valign=top style='width:208.45pt;border:solid windowtext 1.0pt;
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solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>Production activities<o:p></o:p></span></b></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>

</tr> <tr style='mso-yfti-irow:1;height:15.1pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>x1<o:p></o:p></span></b></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>x2<o:p></o:p></span></b></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>x3<o:p></o:p></span></b></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>x4<o:p></o:p></span></b></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>

</tr> <tr style='mso-yfti-irow:2;height:15.1pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><b
style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:10.0pt;
mso-ansi-language:EN-GB'>Objective function <o:p></o:p></span></b></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>

</tr> <tr style='mso-yfti-irow:3;height:15.1pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>Expected gross
margin (pesos)<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>253<o:p></o:p></span></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>443<o:p></o:p></span></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>284<o:p></o:p></span></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>516<o:p></o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><b
style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:10.0pt;
mso-ansi-language:EN-GB'>Maximize<o:p></o:p></span></b></p>
</td>

</tr> <tr style='mso-yfti-irow:4;height:15.1pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><b
style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:10.0pt;
mso-ansi-language:EN-GB'>Constraints<o:p></o:p></span></b></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>

</tr> <tr style='mso-yfti-irow:5;height:15.1pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>Land (ha)<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>&lt;=<o:p></o:p></span></p>
</td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>200<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:6;mso-yfti-lastrow:yes;height:15.1pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
class=SpellE><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>Labor</span></span><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'> (hours)<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>25<o:p></o:p></span></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>36<o:p></o:p></span></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>27<o:p></o:p></span></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>87<o:p></o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>&lt;=<o:p></o:p></span></p>
</td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>10000<o:p></o:p></span></p>
</td>

</tr> </table>

Source: Own compilation.<o:p></o:p>

<!–[if supportFields]> REF _Ref389667383 \h \* MERGEFORMAT <![endif]–>Table 1<!–[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380039003600360037003300380033000000</w:data> </xml><![endif]–><!–[if supportFields]><![endif]–> presents all the information that is needed to solve a linear programming model. The farmer has to set the level of four production activities that produce four commodities. The objective function is to maximize the expected total gross margin. But at the same time the resource constraints must hold. In particular, at maximum 200 ha of land are available for each production activity and 10,000 hours of labour. Each production activity has the same requirement to the land. This means, one ha of land produces one unit of the commodity. The production activities need different amounts of labour. For example, production activity 4 needs 87 hours of labour to produce one unit of commodity four. This activity has also the greatest expected gross margin of 516 per unit. The combination of the production activities that maximizes the total gross margin and that does not violate the constraints has to be find.<o:p></o:p>

This problem is solved with the solver in Excel. The expected total gross margin <v:shape id=“_x0000_i1046” type=“#_x0000_t75” style='width:9pt;height:11.25pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image021.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1046”

DrawAspect="Content" ObjectID="_1632305232">

</o:OLEObject> </xml><![endif]–> is calculated with <v:shape id=“_x0000_i1047” type=“#_x0000_t75” style='width:150.75pt; height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image022.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1047”

DrawAspect="Content" ObjectID="_1632305233">

</o:OLEObject> </xml><![endif]–>. The constraint of the resource land with <v:shape id=“_x0000_i1048” type=“#_x0000_t75” style='width:96pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image023.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1048”

DrawAspect="Content" ObjectID="_1632305234">

</o:OLEObject> </xml><![endif]–> and the resource of labour with <v:shape id=“_x0000_i1049” type=“#_x0000_t75” style='width:150.75pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image024.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1049”

DrawAspect="Content" ObjectID="_1632305235">

</o:OLEObject> </xml><![endif]–> are binding. The solver of Excel gives the solution of <v:shape id=“_x0000_i1050” type=“#_x0000_t75” style='width:48pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image025.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1050”

DrawAspect="Content" ObjectID="_1632305236">

</o:OLEObject> </xml><![endif]–> and <v:shape id=“_x0000_i1051” type=“#_x0000_t75” style='width:43.5pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image026.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1051”

DrawAspect="Content" ObjectID="_1632305237">

</o:OLEObject> </xml><![endif]–>. The expected total gross margin is 92,607.84 pesos. The resources of land and labour are totally exhausted. The farmer is advised to only use production activity two and four to maximize his profits. The shadow price of land is 391.5 and labour is 1.43. For instance, the representative farmer would pay 391.5 for one additional unit of land to enhance his production level for one of his preferred production activities.<o:p></o:p>

<h3 style='text-align:justify'>Conclusions of the example<o:p></o:p></h3>

This little example shows the easy implementation of the linear programming model to set up a profit maximizing farm production plan. The representative farmer has the knowledge about the expected gross margins and resource requirements of each production activity and with that, the linear programming model is a useful tool to calculate the profit maximizing production plan.<a style='mso-footnote-id:ftn4' href=“#_ftn4” name=“_ftnref4” title=“”><![if !supportFootnotes]><span lang=EN-GB style='font-size:11.0pt;line-height: 115%;font-family:“Calibri”,sans-serif;mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:“Times New Roman”;mso-bidi-theme-font:minor-bidi; mso-ansi-language:EN-GB;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>[4]<![endif]></a><o:p></o:p>

We can see that not all production activities are part of the production problem. But in reality we observe that farmers also use production activities that seem to be less profitable. The linear programming model obviously does not consider real farmer’s behaviour and produces overspecialisation. There can be several reasons why farmers use less profitable production activities. One the one hand there are governmental rules or production activity rotation requirements that force the farmer to set up a less profitable production plan. This could be handled by additional constraints. Further reasons for this behaviour can be the risk aversion of the farmer or some costs that the farmer faces for some production activities that cannot be observed and with that not be implemented with additional constraints. Additionally, implementing more constraints to the linear programming model will increase the problem of overspecialisation.<o:p></o:p>

Especially the problem of unobserved costs for the farmer should be the point we want to investigate in the following. The linear programming model is extended and the solution of the optimization programme should be more realistic when compared to real world behaviour.<o:p></o:p>

<h2 style='text-align:justify'>Positive mathematical programming model <o:p></o:p></h2>

To overcome the problem of overspecialisation and to reflect more realistic behaviour of farmers, positive mathematical programming is a methodology that calibrates programming models to observed quantities to specify appropriate non-linear objective functions (Heckelei, 2002).<a style='mso-footnote-id:ftn5' href=“#_ftn5” name=“_ftnref5” title=“”><![if !supportFootnotes]><span lang=EN-GB style='font-size:11.0pt;line-height:115%;font-family:“Calibri”,sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:“Times New Roman”; mso-bidi-theme-font:minor-bidi;mso-ansi-language:EN-GB;mso-fareast-language: EN-US;mso-bidi-language:AR-SA'>[5]<![endif]></a> These objective functions are modifications of the traditional objective function used in linear programming models and have terms that can be interpreted to capture the unobserved behaviour of the farmer and hence, should lead to more realistic optimization solutions.<o:p></o:p>

The positive mathematical programming approach can be separated into three steps (Howitt, 1995). At first, the optimization model is forced to reproduce observed activity levels. Second, the dual values of the calibration constraints are used for the modification of the objective function. Third, the new model is employed for simulations.<o:p></o:p>

A positive mathematical programming model builds on the basis of the linear programming model and is extended only by additional constraints. These are the calibration constraints:<o:p></o:p>

<!–[if supportFields]> MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTSec \c \* Arabic \* MERGEFORMAT 1. SEQ MTEqn \c \* Arabic \* MERGEFORMAT 4)<![endif]–><![if !supportNestedAnchors]><a name=ZEqnNum382441></a><![endif]><!–[if supportFields]><![endif]–> <v:shape id=“_x0000_i1052” type=“#_x0000_t75” style='width:74.25pt;height:18.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image027.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1052”

DrawAspect="Content" ObjectID="_1632305238">

</o:OLEObject> </xml><![endif]–>

Where:<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1053” type=“#_x0000_t75” style='width:12.75pt;height:18.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image028.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1053”

DrawAspect="Content" ObjectID="_1632305239">

</o:OLEObject> </xml><![endif]–> are the observed production activity levels<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1054” type=“#_x0000_t75” style='width:9pt;height:11.25pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image029.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1054”

DrawAspect="Content" ObjectID="_1632305240">

</o:OLEObject> </xml><![endif]–> is a very small number<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1055” type=“#_x0000_t75” style='width:9pt;height:12.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image030.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1055”

DrawAspect="Content" ObjectID="_1632305241">

</o:OLEObject> </xml><![endif]–> are the dual variables associated with the calibration constraints<o:p></o:p>

The formulas <!–[if supportFields]> GOTOBUTTON ZEqnNum225900 \* MERGEFORMAT REF ZEqnNum225900 \* Charformat \! \* MERGEFORMAT (1.1)<![endif]–><!–[if supportFields]><![endif]–>, <!–[if supportFields]> GOTOBUTTON ZEqnNum136343 \* MERGEFORMAT REF ZEqnNum136343 \* Charformat \! \* MERGEFORMAT (1.2)<![endif]–><!–[if supportFields]><![endif]–>, <!–[if supportFields]> GOTOBUTTON ZEqnNum950209 \* MERGEFORMAT REF ZEqnNum950209 \* Charformat \! \* MERGEFORMAT (1.3)<![endif]–><!–[if supportFields]><![endif]–> and <!–[if supportFields]> GOTOBUTTON ZEqnNum382441 \* MERGEFORMAT REF ZEqnNum382441 \* Charformat \! \* MERGEFORMAT (1.4)<![endif]–><!–[if supportFields]><![endif]–> build the positive mathematical programming model. In the first step, the optimal solution of this positive mathematical programme is forced to exactly reproduce the observed production activity levels (<v:shape id=“_x0000_i1056” type=“#_x0000_t75” style='width:12.75pt;height:18.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image028.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1056”

DrawAspect="Content" ObjectID="_1632305242">

</o:OLEObject> </xml><![endif]–>). The resource constraints <!–[if supportFields]> GOTOBUTTON ZEqnNum136343 \* MERGEFORMAT REF ZEqnNum136343 \* Charformat \! \* MERGEFORMAT (1.2)<![endif]–><!–[if supportFields]><![endif]–> are still binding. <o:p></o:p>

The production activities can be distinguished into preferable and marginal activities. Preferable production activities (<v:shape id=“_x0000_i1057” type=“#_x0000_t75” style='width:12pt;height:13.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image031.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1057”

DrawAspect="Content" ObjectID="_1632305243">

</o:OLEObject> </xml><![endif]–>) are constrained by the calibration constraints and the marginal activities (<v:shape id=“_x0000_i1058” type=“#_x0000_t75” style='width:13.5pt;height:13.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image032.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1058”

DrawAspect="Content" ObjectID="_1632305244">

</o:OLEObject> </xml><![endif]–>) are constrained by the resource constraints. The shadow prices of the calibration constraints are zero for the marginal activities (<v:shape id=“_x0000_i1059” type=“#_x0000_t75” style='width:36.75pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image033.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1059”

DrawAspect="Content" ObjectID="_1632305245">

</o:OLEObject> </xml><![endif]–>) and equal to the difference of gross margin and marginal cost for preferable activities (<v:shape id=“_x0000_i1060” type=“#_x0000_t75” style='width:59.25pt; height:18.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image034.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1060”

DrawAspect="Content" ObjectID="_1632305246">

</o:OLEObject> </xml><![endif]–>). The shadow prices of the resource constraints depend on the objective function entries and the coefficients of the marginal activities ( <v:shape id=“_x0000_i1061” type=“#_x0000_t75” style='width:57pt;height:18.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image035.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1061”

DrawAspect="Content" ObjectID="_1632305247">

</o:OLEObject> </xml><![endif]–> ).<o:p></o:p>

As the shadow prices of the resources only depend on the marginal activities, interaction between the production activities are not covered. With the dual values of the calibration constraints, the mis-specification of the linear model is captured.<o:p></o:p>

In the second step of the positive mathematical programming approach the dual values of the preferable activities (<v:shape id=“_x0000_i1062” type=“#_x0000_t75” style='width:12.75pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image036.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1062”

DrawAspect="Content" ObjectID="_1632305248">

</o:OLEObject> </xml><![endif]–>) are used for the specification of a non-linear objective function. The extension of the former objective function of the linear programming model implies a variable cost function which leads to the omission of the calibration constraints of the mathematical programming model in the first step.<o:p></o:p>

It is now the objective to find the parameters of a variable cost function such that the economic rule marginal revenue equals marginal cost holds at observed activity levels. Most often, a quadratic cost function is used.<o:p></o:p>

In general, a quadratic cost function can be specified like:<o:p></o:p>

<!–[if supportFields]> MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTSec \c \* Arabic \* MERGEFORMAT 1. SEQ MTEqn \c \* Arabic \* MERGEFORMAT 5)<![endif]–><!–[if supportFields]><![endif]–> <v:shape id=“_x0000_i1063” type=“#_x0000_t75” style='width:110.25pt;height:33.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image037.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1063”

DrawAspect="Content" ObjectID="_1632305249">

</o:OLEObject> </xml><![endif]–>

Where:<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1064” type=“#_x0000_t75” style='width:9pt;height:12.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image038.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1064”

DrawAspect="Content" ObjectID="_1632305250">

</o:OLEObject> </xml><![endif]–> are the parameters of the linear cost term<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1065” type=“#_x0000_t75” style='width:15pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image039.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1065”

DrawAspect="Content" ObjectID="_1632305251">

</o:OLEObject> </xml><![endif]–> give the parameters of the quadratic cost term<o:p></o:p>

The marginal variable cost function (<v:shape id=“_x0000_i1066” type=“#_x0000_t75” style='width:21.75pt;height:15pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image040.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1066”

DrawAspect="Content" ObjectID="_1632305252">

</o:OLEObject> </xml><![endif]–>) is the first derivative of the variables cost function (<v:shape id=“_x0000_i1067” type=“#_x0000_t75” style='width:12.75pt;height:15pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image041.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1067”

DrawAspect="Content" ObjectID="_1632305253">

</o:OLEObject> </xml><![endif]–>) with respect to the production activity levels:<o:p></o:p>

<!–[if supportFields]> MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTSec \c \* Arabic \* MERGEFORMAT 1. SEQ MTEqn \c \* Arabic \* MERGEFORMAT 6)<![endif]–><!–[if supportFields]><![endif]–> <v:shape id=“_x0000_i1068” type=“#_x0000_t75” style='width:144.75pt;height:33.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image042.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1068”

DrawAspect="Content" ObjectID="_1632305254">

</o:OLEObject> </xml><![endif]–>

Where:<o:p></o:p>

<![if !supportLists]>-          <![endif]><v:shape id=“_x0000_i1069” type=“#_x0000_t75” style='width:11.25pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image043.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1069”

DrawAspect="Content" ObjectID="_1632305255">

</o:OLEObject> </xml><![endif]–> is the per unit cost of the production activity<o:p></o:p>

The term <v:shape id=“_x0000_i1070” type=“#_x0000_t75” style='width:7.5pt;height:12pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image044.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1070”

DrawAspect="Content" ObjectID="_1632305256">

</o:OLEObject> </xml><![endif]–> can be easily derived: the per unit cost is the difference between the gross margin and the price of the production activity: <v:shape id=“_x0000_i1071” type=“#_x0000_t75” style='width:45.75pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image045.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1071”

DrawAspect="Content" ObjectID="_1632305257">

</o:OLEObject> </xml><![endif]–> with <v:shape id=“_x0000_i1072” type=“#_x0000_t75” style='width:9pt;height:12.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image046.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1072”

DrawAspect="Content" ObjectID="_1632305258">

</o:OLEObject> </xml><![endif]–> as the price.<o:p></o:p>

This variable cost function does not consider the opportunity cost of the fixed resources. But the resource constraints of the complete model count for this.<o:p></o:p>

The final model at the end of step two contains the quadratic cost function in the objective function:<o:p></o:p>

<!–[if supportFields]> MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTSec \c \* Arabic \* MERGEFORMAT 1. SEQ MTEqn \c \* Arabic \* MERGEFORMAT 7)<![endif]–><!–[if supportFields]><![endif]–> <v:shape id=“_x0000_i1073” type=“#_x0000_t75” style='width:145.5pt;height:32.25pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image047.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1073”

DrawAspect="Content" ObjectID="_1632305259">

</o:OLEObject> </xml><![endif]–>

and also the constraints <!–[if supportFields]> GOTOBUTTON ZEqnNum136343 \* MERGEFORMAT REF ZEqnNum136343 \* Charformat \! \* MERGEFORMAT (1.2)<![endif]–><!–[if supportFields]><![endif]–> and <!–[if supportFields]> GOTOBUTTON ZEqnNum950209 \* MERGEFORMAT REF ZEqnNum950209 \* Charformat \! \* MERGEFORMAT (1.3)<![endif]–><!–[if supportFields]><![endif]–> from the linear programming model. The dual values of <!–[if supportFields]> GOTOBUTTON ZEqnNum136343 \* MERGEFORMAT REF ZEqnNum136343 \* Charformat \! \* MERGEFORMAT (1.2)<![endif]–><!–[if supportFields]><![endif]–> are the same as in the optimal solution of the linear programming model.<o:p></o:p>

The number parameters of the new objective function that satisfy the conditions to calibrate to observed activity levels when solving the positive mathematical programming model are infinite. But the different combinations of parameters lead to different response behaviour to changing economic conditions (see Heckelei (2002) for technical proof).<o:p></o:p>

<h3 style='text-align:justify'>Setting the parameters of the new objective function<o:p></o:p></h3>

There are some specification rules to find the parameters of the new objective function.<a style='mso-footnote-id:ftn6' href=“#_ftn6” name=“_ftnref6” title=“”><![if !supportFootnotes]><span lang=EN-GB style='font-size:11.0pt;line-height: 115%;font-family:“Calibri”,sans-serif;mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:“Times New Roman”;mso-bidi-theme-font:minor-bidi; mso-ansi-language:EN-GB;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>[6]<![endif]></a> Some of them are presented in the following (Heckelei, 2002). Here we present only a few. In the CAPRI training course we will elaborate additional specification rules.<o:p></o:p>

One of the earliest specification rules were very simply ¹⁾. Just setting <v:shape id=“_x0000_i1074” type=“#_x0000_t75” style='width:28.5pt; height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image048.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1074”

DrawAspect="Content" ObjectID="_1632305260">

</o:OLEObject> </xml><![endif]–> and all the off-diagonal elements of <v:shape id=“_x0000_i1075” type=“#_x0000_t75” style='width:15pt; height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image049.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1075”

DrawAspect="Content" ObjectID="_1632305261">

</o:OLEObject> </xml><![endif]–> zero, but the diagonal elements as:<o:p></o:p>

<!–[if supportFields]> MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTSec \c \* Arabic \* MERGEFORMAT 1. SEQ MTEqn \c \* Arabic \* MERGEFORMAT 8)<![endif]–><!–[if supportFields]><![endif]–> <v:shape id=“_x0000_i1076” type=“#_x0000_t75” style='width:38.25pt;height:33.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image050.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1076”

DrawAspect="Content" ObjectID="_1632305263">

</o:OLEObject> </xml><![endif]–>

The elements of <v:shape id=“_x0000_i1077” type=“#_x0000_t75” style='width:15pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image051.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1077”

DrawAspect="Content" ObjectID="_1632305264">

</o:OLEObject> </xml><![endif]–> of the marginal activities are zero. The objective function of that specification rule would be:<o:p></o:p>

<!–[if supportFields]> MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTSec \c \* Arabic \* MERGEFORMAT 1. SEQ MTEqn \c \* Arabic \* MERGEFORMAT 9)<![endif]–><![if !supportNestedAnchors]><a name=ZEqnNum923545></a><![endif]><!–[if supportFields]><![endif]–> <v:shape id=“_x0000_i1078” type=“#_x0000_t75” style='width:150pt;height:33.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image052.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1078”

DrawAspect="Content" ObjectID="_1632305265">

</o:OLEObject> </xml><![endif]–>

However, Paris (1988) specified the objective function with another rule. He set <v:shape id=“_x0000_i1079” type=“#_x0000_t75” style='width:28.5pt; height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image053.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1079”

DrawAspect="Content" ObjectID="_1632305266">

</o:OLEObject> </xml><![endif]–> as well as the off-diagonal elements of <v:shape id=“_x0000_i1080” type=“#_x0000_t75” style='width:15pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image054.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1080”

DrawAspect="Content" ObjectID="_1632305267">

</o:OLEObject> </xml><![endif]–>. The diagonal elements are calculated by:<o:p></o:p>

<!–[if supportFields]> MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTSec \c \* Arabic \* MERGEFORMAT 1. SEQ MTEqn \c \* Arabic \* MERGEFORMAT 10)<![endif]–><!–[if supportFields]><![endif]–> <v:shape id=“_x0000_i1081” type=“#_x0000_t75” style='width:54pt;height:33.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image055.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1081”

DrawAspect="Content" ObjectID="_1632305268">

</o:OLEObject> </xml><![endif]–>

This means, that the elements of <v:shape id=“_x0000_i1082” type=“#_x0000_t75” style='width:15pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image054.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1082”

DrawAspect="Content" ObjectID="_1632305269">

</o:OLEObject> </xml><![endif]–> of the marginal activities are not zero as before and the new objective function would be:<o:p></o:p>

<!–[if supportFields]> MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTSec \c \* Arabic \* MERGEFORMAT 1. SEQ MTEqn \c \* Arabic \* MERGEFORMAT 11)<![endif]–><![if !supportNestedAnchors]><a name=ZEqnNum279523></a><![endif]><!–[if supportFields]><![endif]–> <v:shape id=“_x0000_i1083” type=“#_x0000_t75” style='width:137.25pt;height:33.75pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image056.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1083”

DrawAspect="Content" ObjectID="_1632305270">

</o:OLEObject> </xml><![endif]–>

<h3 style='text-align:justify'>Applying the positive mathematical programming approach <o:p></o:p></h3>

The two presented examples of how to specify the new objective function in the positive mathematical programming model is now applied and the results are presented regarding the parameters of the cost functions.<o:p></o:p>

<!–[if supportFields]> REF _Ref390349518 \h \* MERGEFORMAT <![endif]–>Table 2<!–[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300390030003300340039003500310038000000</w:data> </xml><![endif]–><!–[if supportFields]><![endif]–> presents the programming tableau of a positive mathematical programming model. It is quite the same as in the linear programming model of <!–[if supportFields]> REF _Ref389667383 \h \* MERGEFORMAT <![endif]–>Table 1<!–[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380039003600360037003300380033000000</w:data> </xml><![endif]–><!–[if supportFields]><![endif]–>. There are two differences. First, it is convenient to split the gross margin into price and cost per unit of a level of production activity. Second – and this is important for the positive mathematical programming approach – the addition of 4 calibration constraints. The model is forced to solve this optimization problem to have the observed production activity levels (x1=55; x2=30; x3=85 and x4=30) recalibrated. <o:p></o:p>

<a name=“_Ref390349518”>Table </a><!–[if supportFields]> SEQ Table \* ARABIC <![endif]–>2<!–[if supportFields]><![endif]–>: Programming tableau of a positive mathematical programming model (Excel file sheet “PMP reveal dual values”, GAMS file model “Howitt_1”)<o:p></o:p>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=278 nowrap colspan=4 valign=top style='width:208.45pt;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>Production activities<o:p></o:p></span></b></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>

</tr> <tr style='mso-yfti-irow:1;height:15.1pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>x1<o:p></o:p></span></b></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>x2<o:p></o:p></span></b></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>x3<o:p></o:p></span></b></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><b style='mso-bidi-font-weight:normal'><span lang=EN-GB
style='font-size:10.0pt;mso-ansi-language:EN-GB'>x4<o:p></o:p></span></b></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.1pt'></td>

</tr> <tr style='mso-yfti-irow:2;height:13.4pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:13.4pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><b
style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:10.0pt;
mso-ansi-language:EN-GB'>Objective function <o:p></o:p></span></b></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:13.4pt'></td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:13.4pt'></td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:13.4pt'></td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:13.4pt'></td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:13.4pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:13.4pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><b
style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:10.0pt;
mso-ansi-language:EN-GB'>Maximize<o:p></o:p></span></b></p>
</td>

</tr> <tr style='mso-yfti-irow:3;height:11.5pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:11.5pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>Price<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=bottom style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri'>293<o:p></o:p></span></p>
</td>
<td width=67 nowrap valign=bottom style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri'>503<o:p></o:p></span></p>
</td>
<td width=59 nowrap valign=bottom style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri'>319<o:p></o:p></span></p>
</td>
<td width=75 nowrap valign=bottom style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri'>596<o:p></o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.5pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.5pt'></td>

</tr> <tr style='mso-yfti-irow:4;height:9.6pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:9.6pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>Cost<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=bottom style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.6pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri'>40<o:p></o:p></span></p>
</td>
<td width=67 nowrap valign=bottom style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.6pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri'>60<o:p></o:p></span></p>
</td>
<td width=59 nowrap valign=bottom style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.6pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri'>35<o:p></o:p></span></p>
</td>
<td width=75 nowrap valign=bottom style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.6pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri'>80<o:p></o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.6pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><span lang=EN-GB style='font-size:10.0pt;
mso-ansi-language:EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.6pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:5;height:7.2pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:7.2pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><b
style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:10.0pt;
mso-ansi-language:EN-GB'>Constraints<o:p></o:p></span></b></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.2pt'></td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.2pt'></td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.2pt'></td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.2pt'></td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.2pt'></td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.2pt'></td>

</tr> <tr style='mso-yfti-irow:6;height:6.0pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:6.0pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>Land (ha)<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.0pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.0pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.0pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.0pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.0pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>&lt;=<o:p></o:p></span></p>
</td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.0pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>200<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:7;height:11.95pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:11.95pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
class=SpellE><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>Labor</span></span><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'> (hours)<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.95pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>25<o:p></o:p></span></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.95pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>36<o:p></o:p></span></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.95pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>27<o:p></o:p></span></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.95pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>87<o:p></o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.95pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>&lt;=<o:p></o:p></span></p>
</td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:11.95pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>10000<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:8;height:10.0pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:10.0pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>PMP1<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.0pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.0pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.0pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.0pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.0pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>&lt;=<o:p></o:p></span></p>
</td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.0pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>55+e<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:9;height:8.85pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:8.85pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>PMP2<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.85pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.85pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.85pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.85pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.85pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>&lt;=<o:p></o:p></span></p>
</td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.85pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>30+e<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:10;height:7.6pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:7.6pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>PMP3<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.6pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.6pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.6pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.6pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.6pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>&lt;=<o:p></o:p></span></p>
</td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.6pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>85+e<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:11;mso-yfti-lastrow:yes;height:6.6pt'>

<td width=164 nowrap valign=top style='width:122.65pt;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:6.6pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>PMP4<o:p></o:p></span></p>
</td>
<td width=76 nowrap valign=top style='width:57.15pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.6pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=67 nowrap valign=top style='width:50.6pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.6pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=59 nowrap valign=top style='width:44.5pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.6pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'><o:p>&nbsp;</o:p></span></p>
</td>
<td width=75 nowrap valign=top style='width:56.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.6pt'>
<p class=MsoNormal align=center style='margin-top:0cm;margin-right:0cm;
margin-bottom:0cm;margin-left:2.4pt;margin-bottom:.0001pt;text-align:center;
line-height:normal'><span lang=EN-GB style='font-size:10.0pt;mso-ansi-language:
EN-GB'>1<o:p></o:p></span></p>
</td>
<td width=32 nowrap valign=top style='width:24.2pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.6pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>&lt;=<o:p></o:p></span></p>
</td>
<td width=134 nowrap valign=top style='width:100.55pt;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.6pt'>
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
margin-left:2.4pt;margin-bottom:.0001pt;text-align:justify;line-height:normal'><span
lang=EN-GB style='font-size:10.0pt;mso-ansi-language:EN-GB'>30+e<o:p></o:p></span></p>
</td>

</tr> </table>

Source: Own compilation.<o:p></o:p>

Now you would optimize the objective function given the constraints. The solution of this optimization problem reveals that only the resource of land is totally exhausted. One should remember that in the linear programming model solution both resources are totally exhausted. In this case, the marginal activity is x1 and the preferred activities are x2, x3 and x4. Therefore, we only have dual values for x2, x3 and x4 and with that; we have only three out of four diagonal elements larger than zero to specify our new objective function. <!–[if supportFields]> REF _Ref390354601 \h \* MERGEFORMAT <![endif]–>Table 3<!–[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300390030003300350034003600300031000000</w:data> </xml><![endif]–><!–[if supportFields]><![endif]–> depicts the parameters of the objective function of <!–[if supportFields]> GOTOBUTTON ZEqnNum923545 \* MERGEFORMAT REF ZEqnNum923545 \* Charformat \! \* MERGEFORMAT (1.9)<![endif]–><!–[if supportFields]><![endif]–>.<a style='mso-footnote-id:ftn7' href=“#_ftn7” name=“_ftnref7” title=“”><![if !supportFootnotes]><span lang=EN-GB style='font-size:11.0pt;line-height: 115%;font-family:“Calibri”,sans-serif;mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:“Times New Roman”;mso-bidi-theme-font:minor-bidi; mso-ansi-language:EN-GB;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>[7]<![endif]></a> <o:p></o:p>

<a name=“_Ref390354601”>Table </a><!–[if supportFields]> SEQ Table \* ARABIC <![endif]–>3<!–[if supportFields]><![endif]–>: Parameters of the objective function <!–[if supportFields]> GOTOBUTTON ZEqnNum923545 \* MERGEFORMAT REF ZEqnNum923545 \* Charformat \! \* MERGEFORMAT (1.9)<![endif]–><!–[if supportFields]><![endif]–> (Excel file sheet “PMP1”, GAMS file model “Howitt_11”)<o:p></o:p>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='font-size:10.0pt;mso-ansi-language:EN-US'>Dual value of
calibration constraints <span style='position:relative;top:5.0pt;mso-text-raise:
-5.0pt'><v:shape id="_x0000_i1084" type="#_x0000_t75" style='width:9pt;
 height:12.75pt' o:ole="">
 <v:imagedata src="Session_B5_Advanced_PMP_example-Dateien/image057.wmz"
  o:title=""/>
</v:shape></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1084"
  DrawAspect="Content" ObjectID="_1632305271">
 </o:OLEObject>
</xml><![endif]--><o:p></o:p></span></b></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Q<o:p></o:p></span></b></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x1<o:p></o:p></span></b></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x2<o:p></o:p></span></b></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x3<o:p></o:p></span></b></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b><span style='font-size:10.0pt'>x4<o:p></o:p></span></b></p>
</td>
<td width="7%" nowrap valign=top style='width:7.64%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:10.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>d<o:p></o:p></span></b></p>
</td>

</tr> <tr style='mso-yfti-irow:1;height:9.0pt'>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:9.0pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>x1<o:p></o:p></span></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><a name="RANGE!P17:S20"><span
style='font-size:10.0pt'>0</span></a><span style='font-size:10.0pt'><o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=bottom style='width:7.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>40<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:2;height:9.2pt'>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:9.2pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><span style='font-size:10.0pt'>190<o:p></o:p></span></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>x2<o:p></o:p></span></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>6.333334<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=bottom style='width:7.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>60<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:3;height:8.7pt'>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:8.7pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><span style='font-size:10.0pt'>31<o:p></o:p></span></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.7pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>x3<o:p></o:p></span></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.7pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.7pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.7pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0.364706<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.7pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=bottom style='width:7.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.7pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>35<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:4;mso-yfti-lastrow:yes;height:3.3pt'>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><span style='font-size:10.0pt'>263<o:p></o:p></span></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>x4<o:p></o:p></span></p>
</td>
<td width="9%" nowrap valign=top style='width:9.46%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=top style='width:11.34%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>8.766667<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=bottom style='width:7.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>80<o:p></o:p></span></p>
</td>

</tr> </table>

Source: Own compilation.<o:p></o:p>

<!–[if supportFields]> REF _Ref390354641 \h \* MERGEFORMAT <![endif]–>Table 4<!–[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300390030003300350034003600340031000000</w:data> </xml><![endif]–><!–[if supportFields]><![endif]–> depicts the parameters of the objective function of <!–[if supportFields]> GOTOBUTTON ZEqnNum279523 \* MERGEFORMAT REF ZEqnNum279523 \* Charformat \! \* MERGEFORMAT (1.11)<![endif]–><!–[if supportFields]><![endif]–>. The difference to the parameters of the specification rule above is, that all diagonal elements of <v:shape id=“_x0000_i1085” type=“#_x0000_t75” style='width:15pt;height:16.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image058.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1085”

DrawAspect="Content" ObjectID="_1632305272">

</o:OLEObject> </xml><![endif]–> are non-zero, but the linear cost term is zero instead – here by definition.<o:p></o:p>

<a name=“_Ref390354641”>Table </a><!–[if supportFields]> SEQ Table \* ARABIC <![endif]–>4<!–[if supportFields]><![endif]–>: Parameters of the objective function <!–[if supportFields]> GOTOBUTTON ZEqnNum279523 \* MERGEFORMAT REF ZEqnNum279523 \* Charformat \! \* MERGEFORMAT (1.11)<![endif]–><!–[if supportFields]><![endif]–> (Excel file sheet “PMP3”, GAMS file model “Paris”)<o:p></o:p>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='font-size:10.0pt;mso-ansi-language:EN-US'>Dual value of
calibration constraints <span style='position:relative;top:5.0pt;mso-text-raise:
-5.0pt'><v:shape id="_x0000_i1086" type="#_x0000_t75" style='width:9pt;
 height:12.75pt' o:ole="">
 <v:imagedata src="Session_B5_Advanced_PMP_example-Dateien/image057.wmz"
  o:title=""/>
</v:shape></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1086"
  DrawAspect="Content" ObjectID="_1632305273">
 </o:OLEObject>
</xml><![endif]--><o:p></o:p></span></b></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Q<o:p></o:p></span></b></p>
</td>
<td width="11%" nowrap valign=top style='width:11.66%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x1<o:p></o:p></span></b></p>
</td>
<td width="11%" nowrap valign=top style='width:11.64%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x2<o:p></o:p></span></b></p>
</td>
<td width="11%" nowrap valign=top style='width:11.64%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x3<o:p></o:p></span></b></p>
</td>
<td width="11%" nowrap valign=top style='width:11.64%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b><span style='font-size:10.0pt'>x4<o:p></o:p></span></b></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>d<o:p></o:p></span></b></p>
</td>

</tr> <tr style='mso-yfti-irow:1;height:4.4pt'>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:4.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:4.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>x1<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.66%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:4.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0.72727273<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:4.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:4.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:4.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:4.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:2;height:5.35pt'>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:5.35pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><span style='font-size:10.0pt'>190<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.35pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>x2<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.66%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.35pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.35pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>8.33333333<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.35pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.35pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.35pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:3;height:5.5pt'>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:5.5pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><span style='font-size:10.0pt'>31<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>x3<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.66%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0.77647059<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:5.5pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:4;mso-yfti-lastrow:yes;height:3.3pt'>

<td width="39%" nowrap valign=top style='width:39.42%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><span style='font-size:10.0pt'>263<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>x4<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.66%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="11%" nowrap valign=bottom style='width:11.64%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>11.4333333<o:p></o:p></span></p>
</td>
<td width="7%" nowrap valign=top style='width:7.0%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>

</tr> </table>

Source: Own compilation.<o:p></o:p>

It should be mentioned that both new objective functions (<!–[if supportFields]> GOTOBUTTON ZEqnNum923545 \* MERGEFORMAT REF ZEqnNum923545 \* Charformat \! \* MERGEFORMAT (1.9)<![endif]–><!–[if supportFields]><![endif]–> and <!–[if supportFields]> GOTOBUTTON ZEqnNum279523 \* MERGEFORMAT REF ZEqnNum279523 \* Charformat \! \* MERGEFORMAT (1.11)<![endif]–><!–[if supportFields]><![endif]–>) each with the constraints <!–[if supportFields]> GOTOBUTTON ZEqnNum136343 \* MERGEFORMAT REF ZEqnNum136343 \* Charformat \! \* MERGEFORMAT (1.2)<![endif]–><!–[if supportFields]><![endif]–> and <!–[if supportFields]> GOTOBUTTON ZEqnNum950209 \* MERGEFORMAT REF ZEqnNum950209 \* Charformat \! \* MERGEFORMAT (1.3)<![endif]–><!–[if supportFields]><![endif]–> recalibrate the observed activity levels (<v:shape id=“_x0000_i1087” type=“#_x0000_t75” style='width:12.75pt;height:13.5pt' o:ole=“”> <v:imagedata src=“Session_B5_Advanced_PMP_example-Dateien/image059.wmz”

o:title=""/>

</v:shape><!–[if gte mso 9]><xml> <o:OLEObject Type=“Embed” ProgID=“Equation.DSMT4” ShapeID=“_x0000_i1087”

DrawAspect="Content" ObjectID="_1632305274">

</o:OLEObject> </xml><![endif]–>) without the calibration constraints and this is what both programming models are intended to do. <o:p></o:p>

<h3 style='text-align:justify'>Simulation behaviour of the two examples regarding prices changes<o:p></o:p></h3>

In this part we want to compare the linear programming model as well as the two positive mathematical programming models simulation behaviour regarding price changes. Therefore, we change the prices and solve the optimization problems of all three models and compare how different the models react.<o:p></o:p>

<!–[if supportFields]> REF _Ref390360515 \h \* MERGEFORMAT <![endif]–>Table 5<!–[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300390030003300360030003500310035000000</w:data> </xml><![endif]–><!–[if supportFields]><![endif]–> depicts the simulated price changes of the commodities of the production activities. Only p1 and p3 are increasing, p2 and p4 are remaining constant. Price p1 increases with 40 units and price p3 with 60 units with each scenario step.<o:p></o:p>

<a name=“_Ref390360515”>Table </a><!–[if supportFields]> SEQ Table \* ARABIC <![endif]–>5<!–[if supportFields]><![endif]–>: Simulated price changes of the commodities for the four production <o:p></o:p>

<td width="21%" nowrap valign=top style='width:21.26%;border:solid windowtext 1.0pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal'><span lang=EN-GB style='mso-ascii-font-family:Calibri;mso-hansi-font-family:
Calibri;mso-bidi-font-family:Calibri;color:black;mso-ansi-language:EN-GB'>&nbsp;<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.7%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>p1<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap style='width:19.7%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>p2<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap style='width:19.68%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>p3<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap style='width:19.66%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:3.3pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>p4<o:p></o:p></span></b></p>
</td>

</tr> <tr style='mso-yfti-irow:1;height:6.4pt'>

<td width="21%" nowrap style='width:21.26%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:6.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b><span style='font-size:10.0pt;mso-ascii-font-family:
Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;
color:black'>Original<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>293<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>503<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.68%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>319<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.66%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:6.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>596<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:2;height:7.8pt'>

<td width="21%" nowrap style='width:21.26%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:7.8pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b><span style='font-size:10.0pt;mso-ascii-font-family:
Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;
color:black'>Scenario 1<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.8pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>333<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.8pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>503<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.68%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.8pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>379<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.66%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:7.8pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>596<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:3;height:8.0pt'>

<td width="21%" nowrap style='width:21.26%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:8.0pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b><span style='font-size:10.0pt;mso-ascii-font-family:
Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;
color:black'>Scenario 2<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>373<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>503<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.68%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>439<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.66%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.0pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>596<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:4;height:8.2pt'>

<td width="21%" nowrap style='width:21.26%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:8.2pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b><span style='font-size:10.0pt;mso-ascii-font-family:
Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;
color:black'>Scenario 3<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>413<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>503<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.68%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>499<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.66%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:8.2pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>596<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:5;mso-yfti-lastrow:yes;height:9.1pt'>

<td width="21%" nowrap style='width:21.26%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:9.1pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b><span style='font-size:10.0pt;mso-ascii-font-family:
Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;
color:black'>Scenario 4<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>453<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.7%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>503<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.68%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:#1F497D'>559<o:p></o:p></span></p>
</td>
<td width="19%" nowrap style='width:19.66%;border-top:none;border-left:none;
border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:9.1pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:
Calibri;color:black'>596<o:p></o:p></span></p>
</td>

</tr> </table>

Source: Own compilation.<o:p></o:p>

Now, all the three optimization models are solved again with the different sets of prices. For the linear programming model, the most profitable levels of production activities for each price scenario depict <!–[if supportFields]> REF _Ref390360889 \h \* MERGEFORMAT <![endif]–>Table 6<!–[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300390030003300360030003800380039000000</w:data> </xml><![endif]–><!–[if supportFields]><![endif]–>. It can easily be seen, that for the first two price scenarios no adaption of the production programme of the representative farmer is profitable. For the other two price scenarios the optimal production were changed to x3=123.3 and x4= 76.7 for scenario 3 and x3=200 for scenario 4.<o:p></o:p>

<a name=“_Ref390360889”>Table </a><!–[if supportFields]> SEQ Table \* ARABIC <![endif]–>6<!–[if supportFields]><![endif]–>: Most profitable levels of production activities of the linear programming model activities (Excel file sheet “Simple LP”, GAMS file model “LP”)<o:p></o:p>

<td width="19%" nowrap valign=top style='width:19.64%;border:solid windowtext 1.0pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'></td>
<td width="19%" nowrap valign=top style='width:19.16%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x1<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x2<o:p></o:p></span></b></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x3<o:p></o:p></span></b></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x4<o:p></o:p></span></b></p>
</td>

</tr> <tr style='mso-yfti-irow:1;height:14.4pt'>

<td width="19%" nowrap valign=top style='width:19.64%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Original<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>145.098<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>54.90196<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:2;height:14.4pt'>

<td width="19%" nowrap valign=top style='width:19.64%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Scenario 1<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>145.098<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>54.90196<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:3;height:14.4pt'>

<td width="19%" nowrap valign=top style='width:19.64%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Scenario 2<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>145.098<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>54.90196<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:4;height:14.4pt'>

<td width="19%" nowrap valign=top style='width:19.64%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Scenario 3<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>123.3333<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>76.66667<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:5;mso-yfti-lastrow:yes;height:14.4pt'>

<td width="19%" nowrap valign=top style='width:19.64%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Scenario 4<o:p></o:p></span></b></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="19%" nowrap valign=top style='width:19.16%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>200<o:p></o:p></span></p>
</td>
<td width="21%" nowrap valign=top style='width:21.02%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0<o:p></o:p></span></p>
</td>

</tr> </table>

Source: Own compilation.<o:p></o:p>

<!–[if supportFields]> REF _Ref390361336 \h \* MERGEFORMAT <![endif]–>Table 7<!–[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300390030003300360031003300330036000000</w:data> </xml><![endif]–><!–[if supportFields]><![endif]–> depicts the most profitable levels of production activities of the model with the objective function <!–[if supportFields]> GOTOBUTTON ZEqnNum923545 \* MERGEFORMAT REF ZEqnNum923545 \* Charformat \! \* MERGEFORMAT (1.9)<![endif]–><!–[if supportFields]><![endif]–>. It can be seen, that the levels of the production activities x1, x2, and x4 are declining whereas the level of production x4 is increasing. Although the price of commodity of production activity x1 is increasing, the optimal level of it is decreasing. This is due to the fact that the gross margin of x3 is increasing even higher than for x1 in every new price scenario.<a style='mso-footnote-id:ftn8' href=“#_ftn8” name=“_ftnref8” title=“”><![if !supportFootnotes]><span lang=EN-GB style='font-size:11.0pt;line-height: 115%;font-family:“Calibri”,sans-serif;mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:“Times New Roman”;mso-bidi-theme-font:minor-bidi; mso-ansi-language:EN-GB;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>[8]<![endif]></a><o:p></o:p>

<a name=“_Ref390361336”>Table </a><!–[if supportFields]> SEQ Table \* ARABIC <![endif]–>7<!–[if supportFields]><![endif]–>: Most profitable levels of production activities of the mathematical programming model with objective function <!–[if supportFields]> GOTOBUTTON ZEqnNum923545 \* MERGEFORMAT REF ZEqnNum923545 \* Charformat \! \* MERGEFORMAT (1.9)<![endif]–><!–[if supportFields]><![endif]–> (Excel file sheet “PMP1”, GAMS file model “Howitt_11”)<o:p></o:p>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'></td>
<td width="13%" nowrap valign=top style='width:13.98%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x1<o:p></o:p></span></b></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x2<o:p></o:p></span></b></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x3<o:p></o:p></span></b></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x4<o:p></o:p></span></b></p>
</td>

</tr> <tr style='mso-yfti-irow:1;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal'><b style='mso-bidi-font-weight:normal'><span style='font-size:10.0pt'>Original<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>55.00<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>30.00<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>85.00<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>30.00<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:2;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal'><b style='mso-bidi-font-weight:normal'><span style='font-size:10.0pt'>Scenario
1<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>11.04<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>23.68<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>139.84<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>25.44<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:3;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal'><b style='mso-bidi-font-weight:normal'><span style='font-size:10.0pt'>Scenario
2<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0.00<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>15.64<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>164.73<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>19.63<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:4;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal'><b style='mso-bidi-font-weight:normal'><span style='font-size:10.0pt'>Scenario
3<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0.00<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>7.02<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>179.57<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>13.40<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:5;mso-yfti-lastrow:yes;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal'><b style='mso-bidi-font-weight:normal'><span style='font-size:10.0pt'>Scenario
4<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0.00<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>0.00<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>192.89<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>7.11<o:p></o:p></span></p>
</td>

</tr> </table>

Source: Own compilation.<o:p></o:p>

<!–[if supportFields]> REF _Ref390361416 \h \* MERGEFORMAT <![endif]–>Table 8<!–[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300390030003300360031003400310036000000</w:data> </xml><![endif]–><!–[if supportFields]><![endif]–> depicts the most profitable levels of production activities of the model with the objective function <!–[if supportFields]> GOTOBUTTON ZEqnNum279523 \* MERGEFORMAT REF ZEqnNum279523 \* Charformat \! \* MERGEFORMAT (1.11)<![endif]–><!–[if supportFields]><![endif]–>. It can be seen that also here only the level of the production activity x3 is increasing. This is also due to the fact that the gross margin of x3 is increasing even higher than for x1 and the other production activities with every new price scenario.<o:p></o:p>

<a name=“_Ref390361416”>Table </a><!–[if supportFields]> SEQ Table \* ARABIC <![endif]–>8<!–[if supportFields]><![endif]–>: Most profitable levels of production activities of the mathematical programming model with objective function <!–[if supportFields]> GOTOBUTTON ZEqnNum279523 \* MERGEFORMAT REF ZEqnNum279523 \* Charformat \! \* MERGEFORMAT (1.11)<![endif]–><!–[if supportFields]><![endif]–> (Excel file sheet “PMP3”, GAMS file model “Paris”)<o:p></o:p>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'></td>
<td width="13%" nowrap valign=top style='width:13.98%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x1<o:p></o:p></span></b></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x2<o:p></o:p></span></b></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x3<o:p></o:p></span></b></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border:solid windowtext 1.0pt;
border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>x4<o:p></o:p></span></b></p>
</td>

</tr> <tr style='mso-yfti-irow:1;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Original<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>55.00<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>30.00<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>85.00<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>30.00<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:2;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Scenario 1<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>46.64<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>24.47<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>102.92<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>25.97<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:3;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Scenario 2<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>38.27<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>18.94<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>120.85<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>21.94<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:4;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Scenario 3<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>29.91<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>13.41<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>138.77<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>17.91<o:p></o:p></span></p>
</td>

</tr> <tr style='mso-yfti-irow:5;mso-yfti-lastrow:yes;height:14.4pt'>

<td width="41%" nowrap valign=top style='width:41.92%;border:solid windowtext 1.0pt;
border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt;
padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:
justify;line-height:normal'><b style='mso-bidi-font-weight:normal'><span
style='font-size:10.0pt'>Scenario 4<o:p></o:p></span></b></p>
</td>
<td width="13%" nowrap valign=top style='width:13.98%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>21.55<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>7.88<o:p></o:p></span></p>
</td>
<td width="15%" nowrap valign=top style='width:15.62%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>156.70<o:p></o:p></span></p>
</td>
<td width="14%" nowrap valign=top style='width:14.24%;border-top:none;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;
mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt;height:14.4pt'>
<p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
text-align:center;line-height:normal'><span style='font-size:10.0pt'>13.88<o:p></o:p></span></p>
</td>

</tr> </table>

Source: Own compilation.<o:p></o:p>

<h3 style='text-align:justify'>Conclusions of simulation<o:p></o:p></h3>

The simulation application shows very clear the differences between the linear and the positive mathematical programming approaches. The reaction of the linear programming model to price changes shows erratic adaptions of the production programme induced by price changes. It takes a while until the production programme changes when the model is optimized. These changes are also very strong. This means that between the second and third price scenario the production programme differs completely and the fourth price scenario induce a production plan with only one production activity. This behaviour seems very unlikely in reality.<o:p></o:p>

The first new objective function (<!–[if supportFields]> GOTOBUTTON ZEqnNum923545 \* MERGEFORMAT REF ZEqnNum923545 \* Charformat \! \* MERGEFORMAT (1.9)<![endif]–><!–[if supportFields]><![endif]–>) of the positive mathematical programming approach shows a smoother reaction to price changes compared to the linear programming model. But it can be seen that the adaption of the production programme is still relatively erratic. But the reaction to price changes seems to be much more likely than in the linear programming model.<o:p></o:p>

The second new objective function (<!–[if supportFields]> GOTOBUTTON ZEqnNum279523 \* MERGEFORMAT REF ZEqnNum279523 \* Charformat \! \* MERGEFORMAT (1.11)<![endif]–><!–[if supportFields]><![endif]–>) shows the most economically sophisticated reaction to price changes compared to the other simulated models. The adaption of the production plan induced by price changes is very smooth and is much more realistic. There is no overspecialisation and overreaction like in the other two models.<o:p></o:p>

<h2 style='text-align:justify'>Conclusion<o:p></o:p></h2>

This paper presents the structure of a simple linear farm production model and the extension based on the positive mathematical programming approach to be able to produce more realistic production plans when it comes to profit maximization. The positive mathematical programming approach calibrates a programming model to observed production behaviour. This is achieved with calibration constraints and the dual values of the calibration constraints are used to specify a new objective function that reflects observed farm behaviour that cannot be captured with additional constraints. These new objective functions capture a lot of possible mis-specifications in linear programming models regarding technology, risk behaviour or other non-linear constraints.<o:p></o:p>

The new objective functions can contain several specifications of cost functions. There a many ways to specify these functions and each of them imply different behaviour to changing economic circumstances. Additionally to the specifications shown in this paper there are others as well. The average-cost-approach (Heckelei, 2002) or the use of exogenous supply elasticities (Heckelei, 2002; empirically applied by Helming et al., 2001) are some of them, which will elaborated in the CAPRI training course in Seville. You can also have a closer look at them in the Excel file sheet “PMP2” and “PMP4” as well as in the GAMS file models “Howitt_12” and “Elasticities1”, respectively.<o:p></o:p>

The procedures presented to specify the objective functions are not unproblematic. As these procedures capture the observed behaviour, a change in economic incentives of the farmer(s) over time inducing other behaviour is not observed and must come from other sources. Other shortcomings of these approaches of positive mathematical programming models can be found in the literature (see Heckelei (2002) for an overview).<o:p></o:p>

<h2 style='text-align:justify'>References<o:p></o:p></h2>

Arfini, F. and Paris, Q. (1995): A positive mathematical programming model for regional analysis of agricultural policies. In: Sotte, E. (Hg.): The Regional Dimension in Agricultural Economics and Policies, EAAE, Proceedings of the 40th Seminar, 26.-28. Juni 1995, Ancona, S. 17-35. <o:p></o:p>

Hazell, P. B. R. & Norton, R. D. (1986): Mathematical Programming for Economic Analysis in Agriculture, Macmillan Publishing Company.<o:p></o:p>

Heckelei, T. (2002): Calibration and estimation of programming models for agricultural supply analysis. Habilitation thesis.<o:p></o:p>

Helming, J. F. M., Peeters, L. and VEENDENDAAL, P.J.J (2001): Assessing the Consequences of Environmental Policy Scenarios in Flemish Agriculture. In: Heckelei, T., Witzke, H.P. and Henrichsmeyer, W. (Eds.): Agricultural Sector Modelling and Policy Information Systems. Proceedings of the 65 th EAAE Seminar, March 29-31, 2000 at Bonn University, Vauk Verlag Kiel, pp. 237-245. <o:p></o:p>

Howitt, R. E. (1995): Positive Mathematical Programming. American Journal of Agricultural Economics, 77, p. 329-342.<o:p></o:p>

Howitt, R.E. and Mean, P. (1983): A Positive Approach to Microeconomic Programming Models. Working Paper (6). Department of Agricultural Economics, University of California, Davis. <o:p></o:p>

Paris, Q. (1988): PQP, PMP, Parametric Programming and Comparative Statics. Chapter 11 in Notes for AE 253. Department of Agricultural Economics, University of California, Davis. <o:p></o:p>

Röhm, O. (2001): Analyse der Produktions- und Einkommenseffekte von Agrarumwelt-programmen unter Verwendung einer weiterentwickelten Form der Positiv Quadratischen Programmierung. Shaker Verlag, Aachen. <o:p></o:p>

Umstetter, J. (1999): Calibrating Regional Production Models using Positive Mathematical Programming. An Agro-environmental Policy Analysis in Southwest Germany. Shaker Verlag, Aachen. <o:p></o:p>

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<a style='mso-footnote-id:ftn1' href=“#_ftnref1” name=“_ftn1” title=“”><![if !supportFootnotes]><span style='font-size:10.0pt;line-height:115%;font-family:“Calibri”,sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:“Times New Roman”; mso-bidi-theme-font:minor-bidi;mso-ansi-language:DE;mso-fareast-language:EN-US; mso-bidi-language:AR-SA'>[1]<![endif]></a> Author: Sebastian Neuenfeldt, Thünen Institute of Farm Economics<o:p></o:p>

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<a style='mso-footnote-id:ftn2' href=“#_ftnref2” name=“_ftn2” title=“”><![if !supportFootnotes]><span style='font-size:10.0pt;line-height:115%;font-family:“Calibri”,sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:“Times New Roman”; mso-bidi-theme-font:minor-bidi;mso-ansi-language:DE;mso-fareast-language:EN-US; mso-bidi-language:AR-SA'>[2]<![endif]></a> The excel file as well as the GAMS file are already completely working. But you must be familiar how to user the solver in excel and how to run a GAMS file. Be careful how to set all the constraints to get the desired behaviour of the models!<o:p></o:p>

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<a style='mso-footnote-id:ftn3' href=“#_ftnref3” name=“_ftn3” title=“”><![if !supportFootnotes]><span style='font-size:10.0pt;line-height:115%;font-family:“Calibri”,sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:“Times New Roman”; mso-bidi-theme-font:minor-bidi;mso-ansi-language:DE;mso-fareast-language:EN-US; mso-bidi-language:AR-SA'>[3]<![endif]></a> You have to activate the “solver” add-in in the options.<o:p></o:p>

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<a style='mso-footnote-id:ftn4' href=“#_ftnref4” name=“_ftn4” title=“”><![if !supportFootnotes]><span lang=EN-GB style='font-size:10.0pt;line-height: 115%;font-family:“Calibri”,sans-serif;mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:“Times New Roman”;mso-bidi-theme-font:minor-bidi; mso-ansi-language:EN-GB;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>[4]<![endif]></a> In general, a linear programming model is an optimization model, in which an objective function is maximized or minimized subject to some constraints. In our case we have a maximization problem which is also called the primal model. The total gross margin is maximized while land and labour use are constrained. This problem can be transformed into a minimization problem (dual model), in which land and labour use has to be minimized while the total gross margins of each activity are constrained to have a certain minimum. The maximum value of the objective function of the primal model is always the same like the value of the objective function of the dual model. See Hazell & Norton (1986) for a more detailed presentation.<o:p></o:p>

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<a style='mso-footnote-id:ftn5' href=“#_ftnref5” name=“_ftn5” title=“”><![if !supportFootnotes]><span style='font-size:10.0pt;line-height:115%;font-family:“Calibri”,sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:“Times New Roman”; mso-bidi-theme-font:minor-bidi;mso-ansi-language:DE;mso-fareast-language:EN-US; mso-bidi-language:AR-SA'>[5]<![endif]></a> Most of this part is based on Heckelei (2002).<o:p></o:p>

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<a style='mso-footnote-id:ftn6' href=“#_ftnref6” name=“_ftn6” title=“”><![if !supportFootnotes]><span style='font-size:10.0pt;line-height:115%;font-family:“Calibri”,sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:“Times New Roman”; mso-bidi-theme-font:minor-bidi;mso-ansi-language:DE;mso-fareast-language:EN-US; mso-bidi-language:AR-SA'>[6]<![endif]></a> See Umstätter (1999) or Röhm (2001).<o:p></o:p>

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<a style='mso-footnote-id:ftn7' href=“#_ftnref7” name=“_ftn7” title=“”><![if !supportFootnotes]><span style='font-size:10.0pt;line-height:115%;font-family:“Calibri”,sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:“Times New Roman”; mso-bidi-theme-font:minor-bidi;mso-ansi-language:DE;mso-fareast-language:EN-US; mso-bidi-language:AR-SA'>[7]<![endif]></a> Each time the Excel solver is used for optimization and an optimal solution is found, you have to choose the “sensitivity analysis report” to extract the dual values of the calibration constraints. In the GAMS file you can see that after a model is solved, the dual values are captured as follows: lambda(J) = CALIBRATION.m(J);.<o:p></o:p>

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<a style='mso-footnote-id:ftn8' href=“#_ftnref8” name=“_ftn8” title=“”><![if !supportFootnotes]><span style='font-size:10.0pt;line-height:115%;font-family:“Calibri”,sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:“Times New Roman”; mso-bidi-theme-font:minor-bidi;mso-ansi-language:DE;mso-fareast-language:EN-US; mso-bidi-language:AR-SA'>[8]<![endif]></a> And also even higher compared to the other production activities.<o:p></o:p>

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¹⁾

e.g. Howitt and Mean, 1983; Arfini and Paris, 1995