The Porsche Club of America sponsors driver education events that provide highperformance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. DeeganIndustries manufactures two types of roll bars for Porsches. Model DRB is bolted to thecar using existing holes in the car’s frame. Model DRW is a heavier roll bar that must bewelded to the car’s frame. Model DRB requires 20 pounds of a special high-alloy steel, 40minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires25 pounds of the special high-alloy steel, 100 minutes of manufacturing time, and 40minutes of assembly time. Deegan’s steel supplier indicated that at most 40,000 poundsof the high-alloy steel will be available next quarter. In addition, Deegan estimates that2000 hours of manufacturing time and 1600 hours of assembly time will be available nextquarter. The profit contributions are $200 per unit for model DRB and $280 per unit formodel DRW. The linear programming model for this problem is as follows: Maxs.t. 200DRB 1 280DRW20DRB 1 25DRW40DRB 1 100DRW60DRB 1 40DRWDRB, DRW $ 0# 40,000# 120,000# 96,000Steel availableManufacturing minutesAssembly minutesThe 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 poundsof the steel alloy at $2 per pound. Should Deegan purchase the additional pounds ofthe steel alloy? Explain.c. Deegan is considering using overtime to increase the available assembly time. Whatwould you advise Deegan to do regarding this option? Explain.d. Because of increased competition, Deegan is considering reducing the price of modelDRB such that the new contribution to profit is $175 per unit. How would this changein price affect the optimal solution? Explain.e. If the available manufacturing time is increased by 500 hours, will the shadow pricefor the manufacturing time constraint change? Explain.FIGURE 8.21 SENSITIVITY REPORT FOR THE DEEGAN INDUSTRIES PROBLEMVariable CellsModel Final Reduced Objective Allowable AllowableVariable Name Value Cost Coefficient increase decreaseDRB Model DRB 1000.000 0.000 200.000 24.000 88.000DRW Model DRW 800.000 0.000 280.000 220.000 30.000ConstraintsConstraint Final Shadow Constraint Allowable AllowableNumber Name Value price R.H. Side increase decrease1 Steel available 40000.000 8 .800 40000.000 909.091 10000.0002 Manufacturing minutes 120000.000 0.600 120000.000 40000.000 5714.2863 Assembly minutes 92000.000 0.000 96000.000 1E130 4000.000
The Porsche Club of America sponsors driver education events that provide highperformance 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 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
s.t.
200DRB 1 280DRW
20DRB 1 25DRW
40DRB 1 100DRW
60DRB 1 40DRW
DRB, DRW $ 0
# 40,000
# 120,000
# 96,000
Steel available
Manufacturing minutes
Assembly minutes
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
Variable Name Value Cost Coefficient increase decrease
DRB Model DRB 1000.000 0.000 200.000 24.000 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
2 Manufacturing minutes 120000.000 0.600 120000.000 40000.000 5714.286
3 Assembly minutes 92000.000 0.000 96000.000 1E130 4000.000
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