Two-Person Zero-Sum Game (lpsole03)
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/* */
/* 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. */
/* */
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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;