17. The Porsche Club of America sponsors driver education events that provide high- performance driving instruction on actual racetracks. Because safety is a primary con- sideration 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 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:

The sensitivity report is shown in Figure 8.21.

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 shadow price
for the manufacturing time constraint change? Explain.
Transcribed Image Text:Problems 345 17. The Porsche Club of America sponsors driver education events that provide high- performance driving instruction on actual racetracks. Because safety is a primary con- sideration 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 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 s.t. 20DRB + 25DRW < 40,000 Steel available 40DRB + 100DRW = 120,000 Manufacturing minutes 60DRB + 40DRW < 96,000 Assembly minutes DRB, DRW =0 The sensitivity report is shown in Figure 8.21. 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 shadow price for the manufacturing time constraint change? Explain. FIGURE 8.21 SENSITIVITY REPORT FOR THE DEEGAN INDUSTRIES PROBLEM Variable Cells Model Final Reduced Objective Allowable Allowable Increase 24.000 Variable Name Value Cost Coefficient Decrease DRB Model DRB 1000.000 0.000 200.000 88.000 DRW Model DRW 800.000 0.000 280.000 220.000 30.000 Constraints Constraint Final Shadow Constraint Allowable Allowable Number Name Value Price R.H. Side Increase Decrease 1 Steel available 40000.000 8.800 40000.000 909.091 10000.000 Manufacturing minutes Assembly minutes 2 120000.000 0.600 120000.000 40000.000 5714.286 92000.000 0.000 96000.000 1E+30 4000.000

Question

17. The Porsche Club of America sponsors driver education events that provide high- performance driving instruction on actual racetracks. Because safety is a primary con- sideration 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 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:

The sensitivity report is shown in Figure 8.21.

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 shadow price
for the manufacturing time constraint change? Explain.

Problems
345
17. The Porsche Club of America sponsors driver education events that provide high-
performance driving instruction on actual racetracks. Because safety is a primary con-
sideration 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 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
s.t.
20DRB + 25DRW < 40,000 Steel available
40DRB + 100DRW = 120,000 Manufacturing minutes
60DRB + 40DRW < 96,000 Assembly minutes
DRB, DRW =0
The sensitivity report is shown in Figure 8.21.
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 shadow price
for the manufacturing time constraint change? Explain.
FIGURE 8.21 SENSITIVITY REPORT FOR THE DEEGAN INDUSTRIES PROBLEM
Variable Cells
Model
Final
Reduced
Objective
Allowable
Allowable
Increase
24.000
Variable
Name
Value
Cost
Coefficient
Decrease
DRB
Model DRB
1000.000
0.000
200.000
88.000
DRW
Model DRW
800.000
0.000
280.000
220.000
30.000
Constraints
Constraint
Final
Shadow
Constraint
Allowable
Allowable
Number
Name
Value
Price
R.H. Side
Increase
Decrease
1
Steel available
40000.000
8.800
40000.000
909.091
10000.000
Manufacturing minutes
Assembly minutes
2
120000.000
0.600
120000.000
40000.000
5714.286
92000.000
0.000
96000.000
1E+30
4000.000

Accepted Answer

Answered: Image /qna-images/answer/845ddc18-3a2b-4663-aa85-cb75eecd2c3d.jpg