17. 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 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 + 280DRWs.t. 20DRB + 25DRW <=   40,000 Steel available40DRB +100DRW<= 120,000 Manufacturing minutes60DRB + 40DRW <=   96,000 Assembly minutesDRB, DRW >= 0a. Should Deegan purchase the additional pounds of steel alloy?

Question
Asked Nov 16, 2019
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17. 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 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
s.t.
20DRB + 25DRW <=   40,000 Steel available
40DRB +100DRW<= 120,000 Manufacturing minutes
60DRB + 40DRW <=   96,000 Assembly minutes
DRB, DRW >= 0

a. Should Deegan purchase the additional pounds of steel alloy?

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Expert Answer

Step 1

First find the above optimal value by using the graphical method:

 

Find all the extreme point coordinates which are (0, 0), (1600, 0), (1142.86, 685.71), (1000, 800) and (1, 1200) and objective function value corresponding to these coordinates are 0, 320000, 420571.43, 424000, 336000.

 

 

The maximum value of the objectiv...

(0, 2400)
2000
(1000, 800)
1000
(1142.857, 685.714)
(3000, 0)
2000
3000
1000
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(0, 2400) 2000 (1000, 800) 1000 (1142.857, 685.714) (3000, 0) 2000 3000 1000

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