ME30B

Tutorial # 1

17th February, 2004

Max z = 2x₁ – x₂ +  x₃

s.t.    3x₁ + x₂ +  x₃ ≤ 60

         x₁ – x₂ + 2x₃ ≤ 10

         x₁ + x₂ -  x₃ ≤ 20

          x₁, x₂, x₃ ≥ 0

Solution Print Out:

LP OPTIMUM FOUND AT STEP      2

        OBJECTIVE FUNCTION VALUE

        1)      25.00000

  VARIABLE        VALUE          REDUCED COST

        X1        15.000000          0.000000

        X2         5.000000          0.000000

        X3         0.000000          1.500000

       ROW   SLACK OR SURPLUS     DUAL PRICES

        2)        10.000000          0.000000

        3)         0.000000          1.500000

        4)         0.000000          0.500000

Sensitivity Analysis:

 NO. ITERATIONS=       2

 RANGES IN WHICH THE BASIS IS UNCHANGED:

                           OBJ COEFFICIENT RANGES

 VARIABLE         CURRENT        ALLOWABLE        ALLOWABLE

                   COEF          INCREASE         DECREASE

       X1        2.000000         INFINITY         1.000000

       X2       -1.000000         1.000000         1.000000

       X3        1.000000         1.500000         INFINITY

                           RIGHTHAND SIDE RANGES

      ROW         CURRENT        ALLOWABLE        ALLOWABLE

                    RHS          INCREASE         DECREASE

        2       60.000000         INFINITY        10.000000

        3       10.000000        10.000000        30.000000

        4       20.000000         5.000000        10.000000