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Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows: Number of Fans Number of Cooling Coils Economy E Standard S Deluxe D The computer solution is shown below. Variable E S D Constraint 2 2 3 For the coming production period, the company has 260 fan motors, 360 cooling coils, and 2,500 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 63E+ 955 + 1350 S.L. E S D Constraint 1E + 15 + 1E+ 25 + BE+ 125 + E S D profit $ 1 Optimal objective Value 19580.00000 2 3 constraint 2 constraint 3 1 1 160.00000 100.00000 0.00000 to Slack/Surplus 0.00000 0.00000 20.00000 to 1Ds 260 40 s 360 140 s 2,500 E,S, D 20 to 260.00000 360.00000 2500.00000 1 RNS 2 units units units 4 Reduced Cost 0.00000 0.00000 -24.00000 Objective Allowable Allowable Coefficient Increase Decrease 63.00000 12.00000 15.50000 95.00000 31.00000 8.00000 135.00000 24.00000 Infinite (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) to to Manufacturing Time (hours) to 8 12 Fan motors Cooling coils Manufacturing time Dual Value 31.00000 32.00000 0.00000 14 (b) Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be? Allowable Allowable Increase 5.00000 5.00000 (c) Identify the range of feasibility for the right-hand-side values. (If there is no upper or lower limit, enter NO LIMIT.) constraint 1 Decrease 80.00000 100.00000 20.00000

Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows: Number of Fans Number of Cooling Coils Economy E Standard S Deluxe D The computer solution is shown below. Variable E S D Constraint 2 2 3 For the coming production period, the company has 260 fan motors, 360 cooling coils, and 2,500 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 63E+ 955 + 1350 S.L. E S D Constraint 1E + 15 + 1E+ 25 + BE+ 125 + E S D profit $ 1 Optimal objective Value 19580.00000 2 3 constraint 2 constraint 3 1 1 160.00000 100.00000 0.00000 to Slack/Surplus 0.00000 0.00000 20.00000 to 1Ds 260 40 s 360 140 s 2,500 E,S, D 20 to 260.00000 360.00000 2500.00000 1 RNS 2 units units units 4 Reduced Cost 0.00000 0.00000 -24.00000 Objective Allowable Allowable Coefficient Increase Decrease 63.00000 12.00000 15.50000 95.00000 31.00000 8.00000 135.00000 24.00000 Infinite (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) to to Manufacturing Time (hours) to 8 12 Fan motors Cooling coils Manufacturing time Dual Value 31.00000 32.00000 0.00000 14 (b) Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be? Allowable Allowable Increase 5.00000 5.00000 (c) Identify the range of feasibility for the right-hand-side values. (If there is no upper or lower limit, enter NO LIMIT.) constraint 1 Decrease 80.00000 100.00000 20.00000

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section: Chapter Questions
Problem 75P
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Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows: Number of Cooling Coils Economy Standard E Deluxe S D Max s.t. Variable E S D The computer solution is shown below. Constraint 1 2 3 Variable Number of Fans For the coming production period, the company has 260 fan motors, 360 cooling coils, and 2,500 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: 63E+ 955 + 1350 1E + 15 + 1E + 25 + BE 125 + E S D Constraint constraint 1 constraint 2 1 2 3 constraint 3 1 Optimal Objective Value 19580.00000 1 1 E, S, D 20 Value 160.00000 100.00000 0.00000 to to to 1D ≤ 260 4D ≤ 360 = 14D 2,500 ≤ slack/Surplus 63.00000 95.00000 135.00000 0.00000 0.00000 20.00000 RHS Value 260.00000 360.00000 2500.00000 1 2 4 units units units (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) Reduced Cost 0.00000 0.00000 -24.00000 Objective Allowable Allowable Coefficient Increase Decrease 12.00000 31.00000 24.00000 to Manufacturing Time (hours) to 8 12 Fan motors Cooling coils Manufacturing time Dual Value 31.00000 32.00000 0.00000 14 (b) Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be? E S D profit $ (c) Identify the range of feasibility for the right-hand-side values. (If there is no upper or lower limit, enter NO LIMIT.) 15.50000 8.00000 Infinite Allowable Allowable Increase Decrease 5.00000 80.00000 5.00000 100.00000 20.00000 Infinite
Transcribed Image Text:Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows: Number of Cooling Coils Economy Standard E Deluxe S D Max s.t. Variable E S D The computer solution is shown below. Constraint 1 2 3 Variable Number of Fans For the coming production period, the company has 260 fan motors, 360 cooling coils, and 2,500 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: 63E+ 955 + 1350 1E + 15 + 1E + 25 + BE 125 + E S D Constraint constraint 1 constraint 2 1 2 3 constraint 3 1 Optimal Objective Value 19580.00000 1 1 E, S, D 20 Value 160.00000 100.00000 0.00000 to to to 1D ≤ 260 4D ≤ 360 = 14D 2,500 ≤ slack/Surplus 63.00000 95.00000 135.00000 0.00000 0.00000 20.00000 RHS Value 260.00000 360.00000 2500.00000 1 2 4 units units units (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) Reduced Cost 0.00000 0.00000 -24.00000 Objective Allowable Allowable Coefficient Increase Decrease 12.00000 31.00000 24.00000 to Manufacturing Time (hours) to 8 12 Fan motors Cooling coils Manufacturing time Dual Value 31.00000 32.00000 0.00000 14 (b) Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be? E S D profit $ (c) Identify the range of feasibility for the right-hand-side values. (If there is no upper or lower limit, enter NO LIMIT.) 15.50000 8.00000 Infinite Allowable Allowable Increase Decrease 5.00000 80.00000 5.00000 100.00000 20.00000 Infinite
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(d) If the number of fan motors available for production is increased by 35, will the dual value for that constraint change? Explain. Yes, the dual value will change because 35 is greater than the allowable increase of 12. Yes, the dual value will change because 35 is greater than the allowable increase of 5. No, the dual value will not change because there is no upper limit to how much the constraint can increase. No, the dual value will not change because 35 is less than the allowable increase of 265.
Transcribed Image Text:(d) If the number of fan motors available for production is increased by 35, will the dual value for that constraint change? Explain. Yes, the dual value will change because 35 is greater than the allowable increase of 12. Yes, the dual value will change because 35 is greater than the allowable increase of 5. No, the dual value will not change because there is no upper limit to how much the constraint can increase. No, the dual value will not change because 35 is less than the allowable increase of 265.
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