## Finding an Irreducible Infeasible Set (lpsol4)

```/***************************************************************/
/*                                                             */
/*            S A S   S A M P L E   L I B R A R Y              */
/*                                                             */
/*    NAME: lpsol4                                             */
/*   TITLE: Finding an Irreducible Infeasible Set (lpsol4)     */
/* PRODUCT: OR                                                 */
/*  SYSTEM: ALL                                                */
/*    KEYS: OR                                                 */
/*   PROCS: OPTMODEL                                           */
/*    DATA:                                                    */
/*                                                             */
/* SUPPORT:                             UPDATE:                */
/*     REF:                                                    */
/*    MISC: Example 4 from the Linear Programming Solver       */
/*          chapter of Mathematical Programming.               */
/*                                                             */
/***************************************************************/

proc optmodel presolver=none;
/* declare variables */
var x{1..3} >=0;

/* upper bound on variable x[3] */
x[3].ub = 3;

/* objective function */
min obj = x[1] + x[2] + x[3];

/* constraints */
con c1: x[1] + x[2] >= 10;
con c2: x[1] + x[3] <= 4;
con c3: 4 <= x[2] + x[3] <= 5;

solve with lp / iis = on;

print x.status;
print c1.status c2.status c3.status;

/* relax upper bound on constraint c3 */
c3.ub = min{{}}0;

solve with lp / iis = on;

/* print solution */
print x;

quit;

```