Our completed blending model is:

MODEL:

SETS:

  NUTS: SUPPLY;

  BRANDS: PRICE, PRODUCE;

  NCROSSB( NUTS, BRANDS): FORMULA;

ENDSETS

 

DATA:

  NUTS,     SUPPLY =

   PEANUTS   750

   CASHEWS   250;

 

  BRANDS,   PRICE =

   PAWN      2

   KNIGHT    3

   BISHOP    4

   KING      5;

 

  FORMULA = 15 10  6  2

             1  6 10 14;

ENDDATA

 

MAX = @SUM( BRANDS( I): PRICE( I) * PRODUCE( I));

 

@FOR( NUTS( I):

@SUM( BRANDS( J):

 FORMULA( I, J) * PRODUCE( J) / 16) <= SUPPLY( I)

);

END

Model: CHESS

An abbreviated solution report for the model follows:

Global optimal solution found.

Objective value:                   2692.308

Infeasibilities:                   0.000000

Total solver iterations:                  2

 

       Variable     Value    Reduced Cost

 PRODUCE( PAWN)  769.2308       0.0000000

PRODUCE( KNIGHT)  0.000000       0.1538461

PRODUCE( BISHOP)  0.000000       0.7692297E-01

 PRODUCE( KING)  230.7692       0.0000000

 

        Row  Slack or Surplus  Dual Price

         1       2692.308        1.000000

         2       0.000000        1.769231

         3       0.000000        5.461538

Solution to CHESS

This solution tells us Chess should produce 769.2 pounds of the Pawn mix and 230.8 pounds of King for total revenue of $2692.30. Additional interesting information can also be found in the report. The dual prices on the rows indicate Chess should be willing to pay up to $1.77 for an extra pound of peanuts and $5.46 for an extra pound of cashews. If, for marketing reasons, Chess decides it must produce at least some of the Knight and Bishop mixes, then the reduced cost figures tell us revenue will decline by 15.4 cents with the first pound of Knight produced and 7.69 cents with the first pound of Bishop produced.