See the following Management Scientist output. In this problem, we are trying to determine the optimal number of rolls of four types of fabric (1, 2,...

See the following Management Scientist output. In this problem, we are trying to determine the optimal number of rolls of four types of fabric (1, 2, 3, and 4) to produce. Note that the third constraint concerns the available quantity of a certain chemical resin used for each type of fabric, the fourth constraint concerns the available quantity of polyester, and the final two constraints are imposed to ensure that we will incur a $200 penalty if we produce at least 600 units of Types 2 and 4 (since this will require us to redeploy an additional production line).

1. Which constraints are binding?  (2)

_________

1. Which constraint would we prefer to see relaxed? (2)

________

1. Nora in Accounting realized that the profit associated with Type 1 fabric should be $8.00/unit. Will this have an effect on the optimal solution? (2)

Yes_____

No______

1. If the availability of the chemical (third constraint) were 15,000, what effect would this have? (2)

None____

Increase the optimal profit______

Decrease the final profit______

LINEAR PROGRAMMING PROBLEM

MAX 6X1+7X2+4X3+7X4-200X5

    S.T.

      1) 1X1+1X2+1X3<1000

      2) 1X3-1X4>20

      3) 4X1+4X2+3X3+3X4<12000

      4) 3X1+6X2+4X3+5X4<14000

      5) 1X2+1X4-600X5>0

      6) 1X2+1X4-380X5<600

OPTIMAL SOLUTION

Objective Function Value =      10660.000

     Variable            Value            Reduced Costs  

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

        X1                    0.000                  4.474

        X2                    0.000                  4.000

        X3                 1000.000                  0.000

        X4                  980.000                  0.000

        X5                    1.000                  0.000

    Constraint       Slack/Surplus          Dual Prices   

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

        1                     0.000                 10.474

        2                     0.000                 -6.474

        3                  6060.000                  0.000

        4                  5100.000                  0.000

        5                   380.000                  0.000

        6                     0.000                  0.526

OBJECTIVE COEFFICIENT RANGES

  Variable      Lower Limit      Current Value    Upper Limit

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

     X1        No Lower Limit             6.000          10.474

     X2        No Lower Limit             7.000          11.000

     X3                 0.000             4.000  No Upper Limit

     X4                 3.000             7.000  No Upper Limit

     X5             -1900.000          -200.000           0.000

RIGHT HAND SIDE RANGES

 Constraint     Lower Limit      Current Value    Upper Limit

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

      1               620.000          1000.000        1566.667

      2              -636.364            20.000         400.000

      3              5940.000         12000.000  No Upper Limit

      4              8900.000         14000.000  No Upper Limit

      5        No Lower Limit             0.000         380.000

      6               359.333           600.000         980.000