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) 1 8 Economy 1 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 260 fan motors, 300 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: Max 63E+ 95S + 135D s.t. 1E + 1S + 1E + 2S + 8E + 12S + 1D 260 4D 300 14D 2,500 E, S, D 0 Fan motors Cooling coils Manufacturing time The computer solution is shown below. Optimal Objective Value = 17660.00000 Variable Value E 220.00000 S 40.00000 D 0.00000 Constraint 1 2 3 Reduced Cost Slack/Surplus 0.00000 0.00000 260.00000 0.00000 0.00000 -24.00000 Dual Value 31.00000 32.00000 0.00000 Objective Allowable Allowable Variable Coefficient Increase Decrease E 63.00000 12.00000 15.50000 S 95.00000 D 135.00000 31.00000 24.00000 8.00000 Infinite Constraint RHS Value 1 2 3 260.00000 300.00000 2500.00000 Allowable Increase 40.00000 65.00000 Infinite Allowable Decrease 110.00000 40.00000 260.00000 (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) to E S D to to (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 E S D units 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 to (d) If the number of fan motors available for production is increased by 70, will the dual value for that constraint change? Explain. Yes, the dual value will change because 70 is greater than the allowable increase of 12. Yes, the dual value will change because 70 is greater than the allowable increase of 40. No, the dual value will not change because 70 is less than the allowable increase of 300. No, the dual value will not change because there is no upper limit to how much the constraint can increase.