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* Exercise (3): MY FARM Model with sets and sum

*### 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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sets
   COLS /
      wheat
      barley
      rapeseed
      sugarbeet
   /
;

Parameters
   p_uvag(COLS)   gross margin
   p_lab(COLS)    labour quantity
;

p_uvag("wheat")      = 253;
p_uvag("barley")     = 443;
p_uvag("rapeseed")   = 284;
p_uvag("sugarbeet")  = 516;

p_lab("wheat")     = 25;
p_lab("barley")    = 36;
p_lab("rapeseed")  = 27;
p_lab("sugarbeet") = 87;


Variables
  v_obje  objective function value
;

Positive variable
  v_actLevl(COLS)  land area planted with crop
;


Equations
  e_land   land constraint
  e_labour labour constraint
  obje    objective function
;

obje ..            v_obje =E= sum (COLS, v_actLevl(COLS)*p_uvag(COLS));

e_land ..          sum (COLS, v_actLevl(COLS)) =L= 200;

e_labour ..        sum (COLS, p_lab(COLS)*v_actLevl(COLS)) =L= 10000;

Model myfarm /all/;

Solve myfarm using lp maximizing v_obje;