17.              The Porsche Club of America sponsors driver education events that provide high- performance driving instruction on actual race tracks. Because safety is a primary consid- eration 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 ex- isting 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 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 assem- bly 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 man- ufacturing 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 lin- ear programming model for this problem is as follows:

 

Max s.t.

 

200DRB  + 280DRW

 

20DRB  +   25DRW  …   40,000

40DRB + 100DRW  … 120,000

60DRB + 40DRW … 96,000 DRB, DRW  Ú 0

 

 

 

 

Steel available Manufacturing minutes Assembly minutes

 

The computer solution is shown in Figure 3.20.

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? 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 the new contribution to profit is $175 per unit. How would this change in price affect the optimal solution? Explain.

e.               If the available manufacturing time is increased by 500 hours, will the dual value for the manufacturing time constraint change? Explain.

 

FIGURE 3.20     THE SOLUTION FOR THE DEEGAN INDUSTRIES PROBLEM

 

 

 

Variable -------------- DRB	Value --------------- 1000.00000		Reduced Cost ----------------- 0.00000
DRW	800.00000		0.00000
Constraint	Slack/Surplus		Dual Value
--------------	---------------		-----------------
1	0.00000		8.80000
2	0.00000		0.60000
3	4000.00000		0.00000
  Variable	Objective Coefficient	Allowable Increase	Allowable Decrease
----------	------------	----------	----------
DRB	200.00000	24.00000	88.00000
DRW	280.00000	220.00000	30.00000
  Constraint	RHS Value	Allowable Increase	Allowable Decrease
----------	------------	----------	----------
1	40000.00000	909.09091	10000.00000
2	120000.00000	40000.00000	5714.28571
3	96000.00000	Infinite	4000.00000