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 Fans Manufacturing Time (hours) Cooling Coils Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 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: 129 Max 67 E + 93 S + s.t. 1E + 1S + 10 s 250 Fan motors 1E + 25 + 4D 3 360 Cooling coils 1800 Manufacturing time 8E + 12S + 14D s E,S,D 20 Optimal Objective Value = 15780.00000 Variable Value Reduced Cost E 0.00000 S 120.00000 0.00000 60.00000 10.11111 D 0.00000 Constraint Dual Value Fan motors Slack/Surplus 70.00000 0.00000 0.00000 5.22222 Cooling coils Manufacturing time 0.00000 7.72222 Allowable Variable Objective Coefficient Allowable Decrease Increase E 67.00000 9.10000 6.71429 10.11111 S Infinite 93.00000 129.00000 D 139.00000 11.75000 RHS Allowable Allowable Constraint Value Increase Decrease 250.00000 70.00000 Fan motors Cooling coils Manufacturing time Infinite 154.28570 360.00000 135.00000 1800.00000 420.00000 540.00000 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 E 47.5 X 75 X S 87 X 126 X D NA X 159 x b. Suppose the profit for the economy model (E) is increased by $6 per unit, the profit for the standard model (S) is decreased by $2 per unit, and the profit for the deluxe model (D) is 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 "0". Optimal Solution E 80 x S 120 X D 0 If required, round your answer for Total Profit to two decimal places. Total Profit: $ 16,680 X 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 Constraints lower limit upper limit Fan motors 160 280 X Cooling coils 200 X 400 x Manufacturing time 2080 X NA X d. If the number of manufacturing time available for production is increased by 440, will the dual value for that constraint change? Yes because the allowable increase for manufacturing time is 480 X without changing the optimal solution