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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 Standard Deluxe Max s.t. 63E+ 95S + 1E+1S + 1E + 2S + 8E + 12S + Variable E S D Constraint 1 The computer solution is shown below. 2 3 1 Variable E $ D 1 For the coming production period, the company has 240 fan motors, 340 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 profit? The linear programming model for the problem is as follows: 135D Constraint 1 1 Optimal Objective Value 18320.00000 2 3 Value 140.00000 100.00000 0.00000 1 Slack/Surplus 2 0.00000 0.00000 180.00000 4 Fan motors 1D S 240 4D S 340 Cooling coils 14D ≤ 2,500 Manufacturing time E, S, D 20 63.00000 95.00000 135.00000 RHS Value 240.00000 340.00000 2500.00000 Reduced Cost 0.00000 ( 0.00000 -24.00000 Manufacturing Time (hours) 8 12 Dual Value 31.00000 32.00000 0.00000 14 Objective Allowable Allowable Coefficient Increase Decrease 12.00000 31.00000 24.00000 15.50000 8.00000 Infinite Allowable Increase 45.00000 70.00000 45.00000 100.00000 Infinite 180.00000 Allowable Decrease order to maximize

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 Standard Deluxe Max s.t. 63E+ 95S + 1E+1S + 1E + 2S + 8E + 12S + Variable E S D Constraint 1 The computer solution is shown below. 2 3 1 Variable E $ D 1 For the coming production period, the company has 240 fan motors, 340 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 profit? The linear programming model for the problem is as follows: 135D Constraint 1 1 Optimal Objective Value 18320.00000 2 3 Value 140.00000 100.00000 0.00000 1 Slack/Surplus 2 0.00000 0.00000 180.00000 4 Fan motors 1D S 240 4D S 340 Cooling coils 14D ≤ 2,500 Manufacturing time E, S, D 20 63.00000 95.00000 135.00000 RHS Value 240.00000 340.00000 2500.00000 Reduced Cost 0.00000 ( 0.00000 -24.00000 Manufacturing Time (hours) 8 12 Dual Value 31.00000 32.00000 0.00000 14 Objective Allowable Allowable Coefficient Increase Decrease 12.00000 31.00000 24.00000 15.50000 8.00000 Infinite Allowable Increase 45.00000 70.00000 45.00000 100.00000 Infinite 180.00000 Allowable Decrease order to maximize

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) no limit X to no limit no limit X to no limit no limit to no limit E S D X X X (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? units units units 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.) constraint 1 X to no limit X no limit no limit no limit constraint 2 constraint 3 X Xto no limit X to no limit (d) If the number of fan motors available for production is increased by 65, will the dual value for that constraint change? Explain. O Yes, the dual value will change because 65 is greater than the allowable increase of 12. Ⓒ Yes, the dual value will change because 65 is greater than the allowable increase of 45. O No, the dual value will not change because there is no upper limit to how much the constraint can increase. O No, the dual value will not change because 65 is less than the allowable increase of 285.
Transcribed Image Text:(a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) no limit X to no limit no limit X to no limit no limit to no limit E S D X X X (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? units units units 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.) constraint 1 X to no limit X no limit no limit no limit constraint 2 constraint 3 X Xto no limit X to no limit (d) If the number of fan motors available for production is increased by 65, will the dual value for that constraint change? Explain. O Yes, the dual value will change because 65 is greater than the allowable increase of 12. Ⓒ Yes, the dual value will change because 65 is greater than the allowable increase of 45. O No, the dual value will not change because there is no upper limit to how much the constraint can increase. O No, the dual value will not change because 65 is less than the allowable increase of 285.
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 Standard Deluxe Max s.t. 63E + 95S + 1 1E 1S + 1E + 2S + 8E+12S + Variable E S D 1 Constraint 1 2 3 1 Variable E S D Constraint 1 For the coming production period, the company has 240 fan motors, 340 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: The computer solution is shown below. 3 135D E, S, D 20 Optimal Objective Value = 18320.00000 1D ≤ 240 4D ≤ 340 14D ≤ 2,500 1 Value 140.00000 100.00000 0.00000 2 4 0.00000 0.00000 180.00000 RHS Value 240.00000 340.00000 2500.00000 Reduced Cost 0.00000 0.00000 -24.00000 Manufacturing Time (hours) Slack/Surplus Dual Value 31.00000 32.00000 0.00000 8 Fan motors Cooling coils Manufacturing time 12 Allowable Increase 45.00000 45.00000 Infinite 14 Objective Allowable Allowable Coefficient Decrease 15.50000 63.00000 95.00000 Increase 12.00000 31.00000 24.00000 8.00000 Infinite 135.00000 Allowable Decrease 70.00000 100.00000 180.00000
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 Fans Number of Cooling Coils Economy Standard Deluxe Max s.t. 63E + 95S + 1 1E 1S + 1E + 2S + 8E+12S + Variable E S D 1 Constraint 1 2 3 1 Variable E S D Constraint 1 For the coming production period, the company has 240 fan motors, 340 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: The computer solution is shown below. 3 135D E, S, D 20 Optimal Objective Value = 18320.00000 1D ≤ 240 4D ≤ 340 14D ≤ 2,500 1 Value 140.00000 100.00000 0.00000 2 4 0.00000 0.00000 180.00000 RHS Value 240.00000 340.00000 2500.00000 Reduced Cost 0.00000 0.00000 -24.00000 Manufacturing Time (hours) Slack/Surplus Dual Value 31.00000 32.00000 0.00000 8 Fan motors Cooling coils Manufacturing time 12 Allowable Increase 45.00000 45.00000 Infinite 14 Objective Allowable Allowable Coefficient Decrease 15.50000 63.00000 95.00000 Increase 12.00000 31.00000 24.00000 8.00000 Infinite 135.00000 Allowable Decrease 70.00000 100.00000 180.00000
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