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Problem 3-13 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $93, and $129, respectively. The production requirements per unit are as follows Number of Number of Manufacturing Time (hours) Fans Cooling Coils Economy Standard Deluxe 12 14 For the coming production period, the company has 250 fan motors, 360 cooling coils, and 1800 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 67E 93S129D s.t. 1E 1S1D 250 Fan motors 1E 2S+4D 360 Cooling coils 8E+12s14D 1800 Manufacturing time E,S,D20 The sensitivity report is shown in the figure below Optimal Objective Value 15780.00000 Value Reduced Cost Variable 0.00000 120.00000 0.00000 60.00000 0.00000 Slack/Surplus Dual Value Constraint Fan motors Cooling coils Manufacturing time 70.00000 0.00000 0.00000 0.00000 5.22222 7 .72222 Objective Allowable Allowable Variable efficient.... 67.00000 93.00000 129.00000 Increase Decrease 6.71429 9.10000 Infinite 11.75000 139.00000 RHS Value 250.00000 360.00000 Allowable Allowable Constraint Increase --ifinite Decrease 70.00000 135.00000 540.00000 Fan motors Cooling coils Manufacturing time 154.28570 1800.00000 420.00000 a. Identify the range of optimality for each objective function coefficient. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Objective Coefficient Range Variable lower limit upper limit b. Suppose the profit or the economy model E S increased by $6 per unit the profit or the standard model S S decreased by 2 per unit and the pro it e deluxe model S increased by $4 per unit. What will the new optimal solution be? If required, round your answers to three decimal places. If your answer is zero, enter "O". Optimal Solution If required, round your answer for Total Profit to two decimal places. Total Profit: $ c. Identify the range of feasibility for the right-hand-side values. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Right-Hand-Side-Range lower limit upper limit Constraints Fan motors Cooling coils Manufacturing time d. If the number of manufacturing time available for production is increased by 440, will the dual value for that constraint change? because the allowable increase for manufacturing time is without changing the optimal solution Problem 3-13 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $93, and $129, respectively. The production requirements per unit are as follows Number of Number of Manufacturing Time (hours) Fans Cooling Coils Economy Standard Deluxe 12 14 For the coming production period, the company has 250 fan motors, 360 cooling coils, and 1800 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 67E 93S129D s.t. 1E 1S1D 250 Fan motors 1E 2S+4D 360 Cooling coils 8E+12s14D 1800 Manufacturing time E,S,D20 The sensitivity report is shown in the figure below Optimal Objective Value 15780.00000 Value Reduced Cost Variable 0.00000 120.00000 0.00000 60.00000 0.00000 Slack/Surplus Dual Value Constraint Fan motors Cooling coils Manufacturing time 70.00000 0.00000 0.00000 0.00000 5.22222 7 .72222 Objective Allowable Allowable Variable efficient.... 67.00000 93.00000 129.00000 Increase Decrease 6.71429 9.10000 Infinite 11.75000 139.00000 RHS Value 250.00000 360.00000 Allowable Allowable Constraint Increase --ifinite Decrease 70.00000 135.00000 540.00000 Fan motors Cooling coils Manufacturing time 154.28570 1800.00000 420.00000 a. Identify the range of optimality for each objective function coefficient. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Objective Coefficient Range Variable lower limit upper limit b. Suppose the profit or the economy model E S increased by $6 per unit the profit or the standard model S S decreased by 2 per unit and the pro it e deluxe model S increased by $4 per unit. What will the new optimal solution be? If required, round your answers to three decimal places. If your answer is zero, enter "O". Optimal Solution If required, round your answer for Total Profit to two decimal places. Total Profit: $ c. Identify the range of feasibility for the right-hand-side values. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Right-Hand-Side-Range lower limit upper limit Constraints Fan motors Cooling coils Manufacturing time d. If the number of manufacturing time available for production is increased by 440, will the dual value for that constraint change? because the allowable increase for manufacturing time is without changing the optimal solution