Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a...

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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 Manufacturing Time (hours) Economy 1 1 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 220 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: 635 + 955 + Max St. 1350 + ID 220 Fan motors 40 340 Cooling coils 140 2,500 Manufacturing time E, S, DZ D The computer solution is shown below. Optimal Obje Value -19700.00000 Variable Valua Reduced Coat 0.00000 Constraint Slack/Surplus Dual Value Variable Contin 280.00000 Allowable Allevable Allevable Increase 65.00000 I (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) E S D to E (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 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 constraint 2 constraint 3 to to (d) If the number of fan motors available for production is increased by 95, will the dual value for that constraint change? Explain. Yes, the dual value will change because 95 is greater than the allowable increase of 65. O Yes, the dual value will change because 95 is greater than the allowable increase of 12. O No, the dual value will not change because 95 is less than the allowable increase of 285. No, the dual value will not change because there is no upper limit to how much the constraint can increase. 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 Manufacturing Time (hours) Economy 1 1 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 220 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: 635 + 955 + Max St. 1350 + ID 220 Fan motors 40 340 Cooling coils 140 2,500 Manufacturing time E, S, DZ D The computer solution is shown below. Optimal Obje Value -19700.00000 Variable Valua Reduced Coat 0.00000 Constraint Slack/Surplus Dual Value Variable Contin 280.00000 Allowable Allevable Allevable Increase 65.00000 I (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) E S D to E (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 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 constraint 2 constraint 3 to to (d) If the number of fan motors available for production is increased by 95, will the dual value for that constraint change? Explain. Yes, the dual value will change because 95 is greater than the allowable increase of 65. O Yes, the dual value will change because 95 is greater than the allowable increase of 12. O No, the dual value will not change because 95 is less than the allowable increase of 285. No, the dual value will not change because there is no upper limit to how much the constraint can increase.