Note: constraint 4 uses the surplus variable in the initial (infeasible) solution

  MIN     4 X1 + 4 X2 + X3
  SUBJECT TO
         2)   X1 + X2 + X3 <=   2
         3)   2 X1 + X2 <=   3
         4)   2 X1 + X2 + 3 X3 >=   3
  END


 THE TABLEAU

      ROW  (BASIS)         X1        X2        X3  SLK    2  SLK    3
        1 ART           4.000     4.000     1.000     0.000     0.000
        2 SLK    2      1.000     1.000     1.000     1.000     0.000
        3 SLK    3      2.000     1.000     0.000     0.000     1.000
        4 SLK    4     -2.000    -1.000    -3.000     0.000     0.000
 ART      ART          -2.000    -1.000    -3.000     0.000     0.000


      ROW   SLK    4
        1     0.000     0.000
        2     0.000     2.000
        3     0.000     3.000
        4     1.000    -3.000
 ART          0.000    -3.000

       X3 ENTERS AT VALUE   1.0000     IN ROW    4 OBJ. VALUE= -1.0000


 THE TABLEAU

      ROW  (BASIS)         X1        X2        X3  SLK    2  SLK    3
        1 ART           3.333     3.667     0.000     0.000     0.000
        2 SLK    2      0.333     0.667     0.000     1.000     0.000
        3 SLK    3      2.000     1.000     0.000     0.000     1.000
        4       X3      0.667     0.333     1.000     0.000     0.000
 ART      ART           3.333     3.667     0.000     0.000     0.000


      ROW   SLK    4
        1     0.333    -1.000
        2     0.333     1.000
        3     0.000     3.000
        4    -0.333     1.000
 ART          0.333     0.000


 LP OPTIMUM FOUND AT STEP      1

        OBJECTIVE FUNCTION VALUE

        1)      1.000000

  VARIABLE        VALUE          REDUCED COST
        X1         0.000000          3.333333
        X2         0.000000          3.666667
        X3         1.000000          0.000000


       ROW   SLACK OR SURPLUS     DUAL PRICES
        2)         1.000000          0.000000
        3)         3.000000          0.000000
        4)         0.000000         -0.333333

 NO. ITERATIONS=       1


 RANGES IN WHICH THE BASIS IS UNCHANGED:

                           OBJ COEFFICIENT RANGES
 VARIABLE         CURRENT        ALLOWABLE        ALLOWABLE
                   COEF          INCREASE         DECREASE
       X1        4.000000         INFINITY         3.333333
       X2        4.000000         INFINITY         3.666667
       X3        1.000000         5.000000         1.000000

                           RIGHTHAND SIDE RANGES
      ROW         CURRENT        ALLOWABLE        ALLOWABLE
                    RHS          INCREASE         DECREASE
        2        2.000000         INFINITY         1.000000
        3        3.000000         INFINITY         3.000000
        4        3.000000         3.000000         3.000000