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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). Which constraints are binding? Explain. (2) Which constraint would we prefer to see relaxed? Explain. (3) Nora in Accounting realized that the profit associated with Type 1 fabric should be $8.00/unit. What effect would this have on the optimal solution? (3) If the availability of the chemical (third constraint) were 15,000, what effect would this have? (3) 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

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