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 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 Deegans 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 The sensitivity report is shown below Max 200 DBR 280 DRW subject to 20 DRR 25 DRW 40000 Steal available 40 DRB 100 DRW 120000 Manufacturing minutes 60 DRB 40 DRW 96000 Assebmly minutes DRB, DRW 0 Model variable Name Final value Reduced Cost Objective Coefficient Allowable increase Allowable Decrease DRB DRB 1000 000 0 000 200 000 24 000 88 000 DRW DRW 800 000 0 000 280 000 220 000 30 000 Constraint number Name Final value Shadow price Constraint R H Side Allowable Increase Allowable Decrease 1 Steal available 40000 000 8 8000 40000 000 909 091 10000 000 2 Manufacturing minutes 120000 000 0 600 120000 000 40000 000 5714 286 3 Assembly minutes 92000 000 0 000 96000 000 1E 30 4000 000 What are the optimal solution and the total profit contribution (3 marks) 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 (4 marks) c) Deegan is considering using overtime to increase the available assembly time What would you advise Deegan to do regarding this option Explain (4 marks) 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 (3 marks) e) If the available manufacturing time is increased by 500 hours, will the shadow price for the manufacturing time constraint change Explain (3 marks)

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jul 25, 2024

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

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 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. Deegans 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:

The sensitivity report is shown below:

Max. 200 DBR + 280 DRW subject to 20 DRR + 25 DRW 40000 Steal available

40 DRB + 100 DRW 120000 Manufacturing minutes

60 DRB + 40 DRW 96000 Assebmly minutes

DRB, DRW 0

Model variable	Name	Final value	Reduced Cost	Objective Coefficient	Allowable increase	Allowable Decrease
DRB	DRB	1000.000	0.000	200.000	24.000	88.000
DRW	DRW	800.000	0.000	280.000	220.000	30.000

Constraint number	Name	Final value	Shadow price	Constraint R. H. Side	Allowable Increase	Allowable Decrease
1	Steal available	40000.000	8.8000	40000.000	909.091	10000.000
2	Manufacturing minutes	120000.000	0.600	120000.000	40000.000	5714.286
3	Assembly minutes	92000.000	0.000	96000.000	1E + 30	4000.000

What are the optimal solution and the total profit contribution? (3 marks)

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. (4 marks)

c) Deegan is considering using overtime to increase the available assembly time. What would you advise Deegan to do regarding this option? Explain. (4 marks)

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. (3 marks)

e) If the available manufacturing time is increased by 500 hours, will the shadow price for the manufacturing time constraint change? Explain. (3 marks)