The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the car€™s frame. Model DRW is a heavier roll bar that must be welded to the car€™s frame. Model DRB requires 20 pounds of a special high-alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high-alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Deegan€™s steel supplier indicated that at most 40,000 pounds of the high-alloy steel will be available next quarter. In addition, Deegan estimates that 2000 hours of manufacturing time and 1600 hours of assembly time will be available next quarter. The profit contributions are $200 per unit for model DRB and $280 per unit for model DRW. The linear programming model for this problem is as follows:

Max200DRB + 280DRW
s.t.
20DRB + 25DRW ‰¤ 40,000Steel available
40DRB + 100DRW ‰¤ 120,000Manufacturing minutes
60DRB + 40DRW ‰¤ 96,000Assembly minutes
DRB, DRW ‰¥ 0

The Management Scientist solution is shown in Figure.

THE MANAGEMENT SCIENTIST SOLUTION FOR THE DEEGAN INDUSTRIES PROBLEM

a. What are the optimal solution and the total profit contribution?
b. Another supplier offered to provide Deegan Industries with an additional 500 pounds of the steel alloy at $2 per pound. Should Deegan purchase the additional pounds of the steel alloy? Explain.
c. Deegan is considering using overtime to increase the available assembly time. What would you advise Deegan to do regarding this option? Explain.
d. Because of increased competition, Deegan is considering reducing the price of model DRB such that the new contribution to profit is $175 per unit. How would this change in price affect the optimal solution? Explain.
e. If the available manufacturing time is increased by 500 hours, will the dual price for the manufacturing time constraint change?Explain.

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OPTIMAL SOLUTION Obiective Function Value- 424000.000 Variable Value Reduced Costs DRE DRW 1000.000 800.000 0.000 0.000 Constr int Slack/Surplus Dual Prices 0.000 0.000 4000.000 8.800 0.600 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Linit DRB DRW 112.000 250.000 200.000 280.000 224.000 500.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Linit 30000.000 114285 714 92000.000 40000.000 120000.000 40909.091 160000.000 96000.000 No Upper Linit