Question

Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing hotels in the car's frame. Model DRW is a heavier roll bar that must be welded to the cars 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:

Subject to

20DRB + 25DRW ≤ 40,000 Steel available
40DRB + 100DRW ≤ 120,000 Manufacturing minutes
60DRB + 40DRW ≤ 96,000 Assembly minutes
DRB, DRW ≥ 0

a) Obtain a computer solution and find 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 value for
the manufacturing time constraint change? Explain.

Answer 1