Question

1. Given the following linear programming model, answer the questions that follow. You are given the result of a computer program. The results are

Maximize 9 X₁ + 12 X₂ + 10 X₃

Subject to:

Machine Constraint:   3 X₁ + 4 X₂ + 3 X₃ < 160

Labor Constraint:        6 X₁ + 10 X₂ + 4 X₃ < 288

Materials Constraint: 2 X₁ + 2 X₂ + 7 X₃ < 200

Product 2 Constraint: X₁ < 16

OPTIMAL SOLUTION

Objective Function Value =         483.097

      Variable             Value             Reduced Costs  

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

         X1                    16.000                   0.000

         X2                    10.839                   0.000

         X3                    20.903                   0.000

  

     Constraint        Slack/Surplus           Dual Prices   

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

         1                      5.935                   0.000

         2                      0.000                   1.032

         3                      0.000                   0.839

         4                      0.000                   1.129

OBJECTIVE COEFFICIENT RANGES

    Variable       Lower Limit       Current Value     Upper Limit

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

      X1                  7.871              9.000   No Upper Limit

      X2                  2.857             12.000           14.059

      X3                  4.800             10.000           18.750

RIGHT HAND SIDE RANGES

  Constraint      Lower Limit       Current Value     Upper Limit

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

       1                154.065            160.000   No Upper Limit

       2                192.000            288.000          304.727

       3                 70.400            200.000          226.286

       4                  0.000             16.000           30.154

1. If the profit of Product 3 was changed to $20 and the profit of Product 1 was changed $20, would that change the solution?   Provide proof.

2. If the number of minutes of Machine time was decreased to 155 minutes and the amount of materials were decreased to 170 pounds, would this change the solution? Provide proof.

3. The Dual Price for Constraint 1 (Machine time) is 4.2. In terms of this problem what does that mean?

Answer 1