Question: 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

Problem 3-13 (Algorithmic) Quality Air

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 Fans Number of Cooling Coils Manufacturing Time (hours) 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: Max 67E + 935 + 129D s.t. 1E + 15 + 1Ds 250 Fan motors 1E + 25 + 4D s 360 Cooling coils 1800 Manufacturing time 8E + 12S + 14D E,S, D20 The sensitivity report is shown in the figure below. Optimal Objective Value = 15780.00000 Variable Value Reduced Cost ------- --------- E 120.00000 0.00000 S 0.00000 60.00000 10.11111 0.00000 D Constraint Slack/Surplus 70.00000 Dual Value 0.00000 Fan motors Cooling coils Manufacturing time 0.00000 0.00000 5.22222 7.72222 Variable Objective Coefficient Allowable Increase Allowable Decrease E 67.00000 9.10000 Infinite S 6.71429 10.11111 139.00000 93.00000 129.00000 D 11.75000 RHS Allowable Constraint Value Allowable Increase Infinite Decrease Fan motors 250.00000 70.00000 360.00000 Cooling coils Manufacturing time 154.28570 420.00000 135.00000 540.00000 1800.00000 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 (E) is increased $6 per unit, the profit for the standard model (S) is decreased $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 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 Constraints lower limit upper limit 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

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