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* Exercise (2): MyFarm Model
*### The objective of the exercise:
        1) Getting acquainted with the GAMS programming language.

*### The problem:
A farmer wants to maximize his profit using 200 ha of land and 10000 hours of
labor available. He has the option of cultivating three types of crops: wheat,
barley, rapeseed and sugarbeet. The profit received and labor hours required for producing one
ha of each crop are presented in the table below. How much of each crop does he
need to cultivate in order to maximize his profit?


Item                           Wheat Barley Rapeseed Sugarbeet
Profit in euro/ha                253   443     284      516
Required labor hours/ha          25    36      27       87


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Variables
   v_obje  objective function value
;

Positive variables
   v_actLevlWHEAT        land area wheat
   v_actLevlBARLEY       land area barley
   v_actLevlRAPESEED     land area rapeseed
   v_actLevlSUGARBEET    land area sugarbeet
;

Parameters
   p_uvag_wheat              Gross margin of wheat                /253/ ,
   p_uvag_barley             Gross margin of barley               /443/ ,
   p_uvag_rapeseed           Gross margin of rapeseed             /284/ ,
   p_uvag_sugarbeet          Gross margin of sugarbeet            /516/ ,

   p_lab_wheat               Required labor hours of wheat        /25/  ,
   p_lab_barley              Required labor hours of barley       /36/  ,
   p_lab_rapeseed            Required labor hours of rapeseed     /27/  ,
   p_lab_sugarbeet           Required labor hours of sugarbeet    /87/
;


Equations
*Declaration

  e_land   land constraint
  e_labour labour constraint
  obje     objective function
;

*Defintion
obje ..       v_obje =E=     p_uvag_wheat * v_actLevlWHEAT
                           + p_uvag_barley * v_actLevlBARLEY
                           + p_uvag_rapeseed * v_actLevlRAPESEED
                           + p_uvag_sugarbeet * v_actLevlSUGARBEET;

e_land ..     v_actLevlWHEAT + v_actLevlBARLEY + v_actLevlRAPESEED + v_actLevlSUGARBEET =L= 200;

e_labour ..   p_lab_wheat * v_actLevlWHEAT
            + p_lab_barley * v_actLevlBARLEY
            + p_lab_rapeseed * v_actLevlRAPESEED
            + p_lab_sugarbeet * v_actLevlSUGARBEET =L= 10000;



Model myfarm /e_land, e_labour, obje/;

Solve myfarm using lp maximizing v_obje;


display p_lab_barley,p_lab_sugarbeet;
display v_actLevlWHEAT.L, v_actLevlBARLEY.L, v_actLevlRAPESEED.L, v_actLevlSUGARBEET.L;