## Two-Person Zero-Sum Game (lpsole03)

``` /***************************************************************/
/*                                                             */
/*            S A S   S A M P L E   L I B R A R Y              */
/*                                                             */
/*    NAME: lpsole03                                             */
/*   TITLE: Two-Person Zero-Sum Game (lpsole03)                  */
/* PRODUCT: OR                                                 */
/*  SYSTEM: ALL                                                */
/*    KEYS: OR                                                 */
/*   PROCS: OPTMODEL                                           */
/*    DATA:                                                    */
/*                                                             */
/* SUPPORT:                             UPDATE:                */
/*     REF:                                                    */
/*    MISC: Example 3 from the Linear Programming Solver       */
/*          chapter of Mathematical Programming.               */
/*                                                             */
/***************************************************************/

proc optmodel;
num a{1..3, 1..4}=[-5 3 1 8
5 5 4 6
-4 6 0 5];
var x{1..4} >= 0;
max f = sum{i in 1..4}x[i];
con c{i in 1..3}: sum{j in 1..4}a[i,j]*x[j] <= 1;
solve with lp / algorithm = ps presolver = none logfreq = 1;
print x;
print c.dual;
quit;

```