The decision variables represent the amounts of ingredients 1, 2, and 3 to put i

Question

The decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a minimum requirement for ingredient 3. The following model is to be used.

MAX 4X1+6X2+7X3

S.T.

1) 3X1+2X2+5X3<120

2) 1X1+3X2+3X3<80

3) 5X1+5X2+8X3<160

4) 1X3>10

Use the information to solve the problem and generate the sensitivity report.

If the Right hand side of constraint 1 decreased by 20 units and the right hand side of constraint 3 decreased by 25 units, find the solution, the profit and the % from the 100% rule (use 3 decimal places)

The decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a minimum requirement for ingredient 3. The following model is to be used.

MAX 4X1+6X2+7X3

S.T.

1) 3X1+2X2+5X3<120

2) 1X1+3X2+3X3<80

3) 5X1+5X2+8X3<160

4) 1X3>10

Use the information to solve the problem and generate the sensitivity report.

Explanation / Answer

OPTIMAL SOLUTION

Objective Function Value =         166.000

                Variable             Value             Reduced Costs  

                ----------           ----------          ------------------

                    X1                   0.000                   2.000

                    X2                 16.000                   0.000

                    X3                 10.000                   0.000

                Constraint        Slack/Surplus        Dual Prices   

                ------------        ----------------       ----------------

                       1                     38.000                  0.000

                       2                       2.000                  0.000

                       3                       0.000                  1.200

                       4                       0.000                 -2.600

OBJECTIVE COEFFICIENT RANGES

                Variable       Lower Limit       Current Value     Upper Limit

                ----------       ---------------      -----------------     ---------------

                    X1         No Lower Limit          4.000                 6.000

                    X2                  4.375                  6.000        No Upper Limit

                    X3         No Lower Limit          7.000                 9.600

RIGHT HAND SIDE RANGES

              Constraint      Lower Limit       Current Value     Upper Limit

                ------------      ---------------       -----------------    ---------------

                      1                   82.000               120.000             No Upper Limit

                      2                   78.000                 80.000             No Upper Limit

                      3                   80.000               160.000             163.333

                      4                     8.889                 10.000               20.000

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