The OPTLP Procedure

Consider the problem of diet optimization. There are six different foods: bread, milk, cheese, potato, fish, and yogurt. The cost and nutrition values per unit are displayed in Table 6.3.

The objective is to find a minimum-cost diet that contains at least 300 calories, not more than 10 grams of protein, not less than 10 grams of carbohydrates, and not less than 8 grams of fat. In addition, the diet should contain at least 0.5 unit of fish and no more than 1 unit of milk.

You can use the following SAS code to create the MPS-format input data table:

data mycas.ex3;
   input _id_ field1 $ field2 $ field3 $ field4 field5 $ field6;
   datalines;
1  NAME        .          EX3      .     .         .
2  ROWS        .          .        .     .         .
3  N           diet       .        .     .         .
4  G           calories   .        .     .         .
5  L           protein    .        .     .         .
6  G           fat        .        .     .         .
7  G           carbs      .        .     .         .
8  COLUMNS     .          .        .     .         .
9  .           br         diet     2     calories  90
10 .           br         protein  4     fat       1
11 .           br         carbs    15    .         .
12 .           mi         diet     3.5   calories  120
13 .           mi         protein  8     fat       5
14 .           mi         carbs    11.7  .         .
15 .           ch         diet     8     calories  106
16 .           ch         protein  7     fat       9
17 .           ch         carbs    .4    .         .
18 .           po         diet     1.5   calories  97
19 .           po         protein  1.3   fat       .1
20 .           po         carbs    22.6  .         .
21 .           fi         diet     11    calories  130
22 .           fi         protein  8     fat       7
23 .           fi         carbs    0     .         .
24 .           yo         diet     1     calories  180
25 .           yo         protein  9.2   fat       1
26 .           yo         carbs    17    .         .
27 RHS         .          .        .     .         .
28 .           .          calories 300   protein   10
29 .           .          fat      8     carbs     10
30 BOUNDS      .          .        .     .         .
31 UP          .          mi       1     .         .
32 LO          .          fi       .5    .         .
33 ENDATA      .          .        .     .         .
;

You can solve the diet problem by using PROC OPTLP as follows:

proc optlp data=mycas.ex3
   presolver = none
   algorithm = ps
   primalout = mycas.ex3pout
   dualout   = mycas.ex3dout
   logfreq   = 1;
run;

The solution summary and the optimal primal solution are displayed in Output 6.3.1.

The cost of the optimal diet is 12.08 units.