$TITLE  TWO-VARIABLE-PROGRAM - MODEL
$OFFUPPER
* This program solves a simple two variable LP with proper GAMS model
*

 SETS
    J products /bands, coils/;

 PARAMETERS
    C(J)  profit per ton for each product
       / bands 25
         coils 30 / 

    A(J)  tons per hour for each product
       / bands 200
         coils 140 / 
      
    U(J)  upperbounds on the products
       / bands 6000
         coils 4000 / ;

 SCALAR HOURS hours of production time available this week /40/ ;

 VARIABLES
       X(J)    number of tons of each product produced
       Z       total profit

  POSITIVE VARIABLE 
       X ;

  EQUATIONS
       COST        define objective function maximimizing profit
       TIME        Inequality constraint
       ULIMIT(J)   Upper bounds on X;

  COST ..        Z  =E=  SUM((J), C(J)*X(J));

  TIME ..        SUM(J, X(J)/A(J) )  =L= HOURS;

  ULIMIT(J) ..      X(J) =L= U(J);


  MODEL  TWOVAR /ALL/ ;

  SOLVE TWOVAR USING LP MAXIMIZING Z ;

  DISPLAY X.L, X.M ;