The Porsche Club of America sponsors driver education events that provide high-performance 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 Porsches. Model DRB 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: Max 200DRB + 280DRWSubject to: 20DRB + 25DRW < 40,000 Steel available 40DRB + 100DRW < 120,000 Manufacturing minutes 60DRB + 40DRW < 96,000 Assembly minutes DRB, DRW > 0 Solve for the following:What are the optimal solution and total profit contribution?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? Explain.

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10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Systems Of Equations And Inequalities

Section6.5: Systems Of Inequalities

Problem 9ECP

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The Porsche Club of America sponsors driver education events that provide high-performance 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 Porsches. Model DRB 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:

Max 200DRB + 280DRW

Subject to:

20DRB + 25DRW < 40,000 Steel available

40DRB + 100DRW < 120,000 Manufacturing minutes

60DRB + 40DRW < 96,000 Assembly minutes

DRB, DRW > 0

Solve for the following:

What are the optimal solution and total profit contribution?
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? Explain.

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