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: Economy Standard Deluxe E S D Max s.t. Variable E S D Number of Fans Constraint 1 1E + 15 + 1E+ 25 + 8E + 125 + The computer solution is shown below. 2 3 Variable. 1 S D 1 profit $ 1 For the coming production period, the company has 260 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 order to maximize profit? The linear programming model for the problem is as follows: 63E+ 95S + 135D Constraint 1 2 3 Optimal Objective Value 18940.00000 E, S, D 20 Number of Cooling Coils Value 180,00000 80.00000 0.00000 1D 260 4D S 340 140 ≤ 2,500 Slack/Surplus 0.00000 0.00000 100.00000 63.00000 95.00000 135.00000 1 RHS Value 2 260.00000 340.00000 2500.00000 4 to Objective Allowable Coefficient Increase to to Reduced Cost 0.00000 0.00000 -24.00000 Manufacturing. Time (hours) Fan motors Cooling coils Manufacturing time Dual Value 31.00000 32.00000 0.00000 12.00000 31.00000 24.00000 8 Allowable Increase 25,00000 25.00000 Infinite 12 14 (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) to to to Allowable. Decrease 15.50000 8.00000 Infinite (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 units S units D units Allowable Decrease 90.00000 80.00000 100,00000 (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 constraint 2 constraint 3. (d) If the number of fan motors available for production is increased by 55, will the dual value for that constraint change? Explain. O Yes, the dual value will change because 55 is greater than the allowable increase of 25. Yes, the dual value will change because 55 is greater than the allowable increase of 12. 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 55 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: Economy Standard Deluxe E S D Max s.t. Variable E S D Number of Fans Constraint 1 1E + 15 + 1E+ 25 + 8E + 125 + The computer solution is shown below. 2 3 Variable. 1 S D 1 profit $ 1 For the coming production period, the company has 260 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 order to maximize profit? The linear programming model for the problem is as follows: 63E+ 95S + 135D Constraint 1 2 3 Optimal Objective Value 18940.00000 E, S, D 20 Number of Cooling Coils Value 180,00000 80.00000 0.00000 1D 260 4D S 340 140 ≤ 2,500 Slack/Surplus 0.00000 0.00000 100.00000 63.00000 95.00000 135.00000 1 RHS Value 2 260.00000 340.00000 2500.00000 4 to Objective Allowable Coefficient Increase to to Reduced Cost 0.00000 0.00000 -24.00000 Manufacturing. Time (hours) Fan motors Cooling coils Manufacturing time Dual Value 31.00000 32.00000 0.00000 12.00000 31.00000 24.00000 8 Allowable Increase 25,00000 25.00000 Infinite 12 14 (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) to to to Allowable. Decrease 15.50000 8.00000 Infinite (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 units S units D units Allowable Decrease 90.00000 80.00000 100,00000 (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 constraint 2 constraint 3. (d) If the number of fan motors available for production is increased by 55, will the dual value for that constraint change? Explain. O Yes, the dual value will change because 55 is greater than the allowable increase of 25. Yes, the dual value will change because 55 is greater than the allowable increase of 12. 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 55 is less than the allowable increase of 285.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...

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