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(a) What is the optimal solution and the total profit contribution (in $)? DRB DRW 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. Yes, there is no surplus of steel so any additional steel that becomes available should be purchased. OYes, the dual value for steel available is 8.8. Each pound of steel will increase profits more than the $2 per pound that the supplier is offering. O No, the dual value for steel available is 0.6. Each pound of steel will not increase profits enough to justify the $2 per pound that the supplier is offering. No, the allowable increase for steel is only 24 pounds, so the additional profits are not applicable for 500 pounds.

(a) What is the optimal solution and the total profit contribution (in $)? DRB DRW 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. Yes, there is no surplus of steel so any additional steel that becomes available should be purchased. OYes, the dual value for steel available is 8.8. Each pound of steel will increase profits more than the $2 per pound that the supplier is offering. O No, the dual value for steel available is 0.6. Each pound of steel will not increase profits enough to justify the $2 per pound that the supplier is offering. No, the allowable increase for steel is only 24 pounds, so the additional profits are not applicable for 500 pounds.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual race tracks. 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 34,000 pounds of the high-alloy steel will be available next quarter. In addition, Deegan estimates that 2,000 hours of manufacturing time and 1,800 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: 200DRB + 280DRW Max s.t. 20DRB + 25DRW ≤ 34,000 40DRB + 100DRW ≤ 120,000 ≤ 108,000 60DRB + 40DRW DRB, DRW > 0 The computer solution is shown below. Optimal Objective Value = 371200.00000 Variable DRB DRW Constraint 1 2 3 Variable DRB DRW Value 400.00000 1040.00000 Slack/Surplus Reduced Cost 0.00000 0.00000 0.00000 0.00000 42400.00000 Steel available Manufacturing minutes Assembly minutes 200.00000 280.00000 Objective Allowable Coefficient Increase 24.00000 220.00000 Dual Value 8.80000 0.60000 0.00000 Allowable Decrease 88.00000 30.00000
Transcribed Image Text:The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual race tracks. 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 34,000 pounds of the high-alloy steel will be available next quarter. In addition, Deegan estimates that 2,000 hours of manufacturing time and 1,800 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: 200DRB + 280DRW Max s.t. 20DRB + 25DRW ≤ 34,000 40DRB + 100DRW ≤ 120,000 ≤ 108,000 60DRB + 40DRW DRB, DRW > 0 The computer solution is shown below. Optimal Objective Value = 371200.00000 Variable DRB DRW Constraint 1 2 3 Variable DRB DRW Value 400.00000 1040.00000 Slack/Surplus Reduced Cost 0.00000 0.00000 0.00000 0.00000 42400.00000 Steel available Manufacturing minutes Assembly minutes 200.00000 280.00000 Objective Allowable Coefficient Increase 24.00000 220.00000 Dual Value 8.80000 0.60000 0.00000 Allowable Decrease 88.00000 30.00000
Constraint 1 2 3 Variable DRB DRW Constraint 1 2 3 Slack/Surplus 0.00000 0.00000 42400.00000 Objective Allowable Coefficient Increase 24.00000 220.00000 200.00000 280.00000 RHS Value Dual Value 8.80000 0.60000 0.00000 34000.00000 120000.00000 108000.00000 Allowable Decrease 88.00000 30.00000 Allowable Increase 9636.36364 16000.00000 Infinite Allowable Decrease 4000.00000 52000.00000 42400.00000 (a) What is the optimal solution and the total profit contribution (in $)? DRB DRW 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. Yes, there is no surplus of steel so any additional steel that becomes available should be purchased. Yes, the dual value for steel available is 8.8. Each pound of steel will increase profits more than the $2 per pound that the supplier is offering. No, the dual value for steel available is 0.6. Each pound of steel will not increase profits enough to justify the $2 per pound that the supplier is offering. No, the allowable increase for steel is only 24 pounds, so the additional profits are not applicable for 500 pounds. No, there is a slack value of 9,636, so additional pounds of steel will not increase profits.
Transcribed Image Text:Constraint 1 2 3 Variable DRB DRW Constraint 1 2 3 Slack/Surplus 0.00000 0.00000 42400.00000 Objective Allowable Coefficient Increase 24.00000 220.00000 200.00000 280.00000 RHS Value Dual Value 8.80000 0.60000 0.00000 34000.00000 120000.00000 108000.00000 Allowable Decrease 88.00000 30.00000 Allowable Increase 9636.36364 16000.00000 Infinite Allowable Decrease 4000.00000 52000.00000 42400.00000 (a) What is the optimal solution and the total profit contribution (in $)? DRB DRW 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. Yes, there is no surplus of steel so any additional steel that becomes available should be purchased. Yes, the dual value for steel available is 8.8. Each pound of steel will increase profits more than the $2 per pound that the supplier is offering. No, the dual value for steel available is 0.6. Each pound of steel will not increase profits enough to justify the $2 per pound that the supplier is offering. No, the allowable increase for steel is only 24 pounds, so the additional profits are not applicable for 500 pounds. No, there is a slack value of 9,636, so additional pounds of steel will not increase profits.
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