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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 $63, $95, and $135, respectively. The production requirements per unit are as follows: Number of Number of Manufacturing Cooling Fans Time (hours) Colls 1 1 8 1 2 12 1 4 14 Economy Standard Deluxe For the coming production period, the company has 240 fan motors, 300 cooling coils, and 2500 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 63E+95 + 1350 s.t. 1E + 15 + 1DS 240 Fan motors 1E + 25+ 4D S 300 Cooling coils Manufacturing BE + 125 + 140 S 2500 time E,S,D 20 The sensitivity report is shown in the figure below. Optimal Objective Value = 17040.00000 Variable E S D Value 180.00000 60.00000 0.00000 Reduced Cost 0.00000 0.00000 24.00000 Constraint Fan motors Cooling coils Manufacturing time Slack/Surplus 0.00000 0.00000 Dual Value 31.00000 32.00000 340.00000 0.00000 Variable Objective Allowable Coefficient Increase 63.00000 1200000 95.00000 31.00000 135.00000 24.00000 Allowable Decrease 15.50000 8.00000 Infinite D Constraint RHS Value 240.00000 300.00000 Allowable Increase 60.00000 35.00000 Allowable Decrease 90.00000 60.00000 Fan motors Cooling coils Manufacturing time 2500.00000 Infinite 340.00000 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 S D b. Suppose the profit for the economy model (5) 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 "o". Optimal Solution E S D 0 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. It 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 cooling coils available for production is increased by 105, will the dual value for that constraint change? because the allowable increase for cooling coils is without changing the optimal solution