# Linear programming and sensitivity analysis

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 cars frame. Model DRW is a heavier roll bar that must be welded to the car's frame. Model DRB requires 20 pounds of special high-alloy steel, 40 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 for model DRB and $280 for model DRW. The linear programming model for this problem is as follows:

Max 200DRB + 280DRW

s.t.

20 DRB + 25 DRW <= 40,000 (steel available)

40 DRB + 10DRW <= 120,000 (Manufacturing minutes)

60DRB + 40DRW <= 96,000 (Assembly minutes)

DRB, DRW >= 0

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?

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.

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Linear programming - optimal solution and profit contributions and analysis

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 cars frame. Model DRW is a heavier roll bar that must be welded to the car's frame. Model DRB requires 20 pounds of special high-alloy steel, 40 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 ...

#### Solution Summary

It provides the model, the solution to the problem, and sensitivity analysis.