Production Rates

   {  Exmpl11.4-1_ProdRate.mpl  }

   {  Hillier and Lieberman, Introduction to Operations Research, 9th ed.  }

   {  Chapter 11.4,  Example 1, Production, Size 5x10, Page 479  }


TITLE
   ProductionRate;

INDEX
   plant := 1..2;
   product:= 1..3;

DATA
   Hours[plant, product] := (3, 4, 2,
                             4, 6, 2);
   Profit[product] := (5, 7, 3);     !Per unit
   Sales[product] := (7, 5, 9);
   M := 999;

DECISION VARIABLES
   rate[product];

BINARY VARIABLES
   y[product];   !Equals 1 if product i is produced
   p;            !Equals 1 if we produce in Plant 2

MODEL
   MAX TotProfit = SUM(product: Profit * rate);

SUBJECT TO
   Produce[product] : rate <= M*y;
   NumPrd : SUM(product: y) <=2;
   Plnt[plant=1] : SUM(product: Hours * rate) <= 30 + M*p;
   Plnt[plant=2] : SUM(product: Hours * rate) <= 40 + M*(1-p);

BOUNDS
   Potenial[product] : rate <= Sales;

END