The Porsche Club of America sponsors driver education events that provide high-performances driving instruction on actual race tracks. 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 porches. Model DRB is bolted to the car using existing holes in the cars frame. Model BRW 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 special high alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. 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:
MAX: 200DRB + 280DRW
s.t.
20DRB + 25DRW < or = to 40,000 Steel Available
40DRB + 100DRW < or = to 120,000 Manufacturing minutes
60DRB + 40DRW < or = to 96,000 Assembly minutes
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 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 ht new contribution to profit is $175 per unit. How would this change in the 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.