I need question 13, question 12 is for background information 12. Quality Air Conditioning manufactures three home air conditioners: an economy model, astandard model, and a deluxe model. The profits per unit are $63, $95, and $135, respec-tively. The production requirements per unit are as follows:Number ofFansManufacturingTime (hours)Number ofCooling CoilsEconomyStandardDeluxe18121121414For the coming production period, the company has 200 fan motors, 320 cooling coils,and 2400 hours of manufacturing time available. How many economy models (E), stan-dard models (S), and deluxe models (D) should the company produce in order to maximizeprofit? The linear programming model for the problem is as follows:Max 63E + 95S + 135Ds.t.1E + 1S +1D< 200Fan motors1E + 2S +Cooling coilsManufacturing time4D < 3208E + 12S + 14D < 2400E, S, D 0 FIGURE 3.17 THE SOLUTION FOR THE QUALITY AIR CONDITIONING PROBLEMOptimal Objective Value =16440.00000VariableValueReduced CostE80.000000.00000S120.000000.00000D0.00000-24.00000ConstraintSlack/SurplusDual Value10.0000031.0000020.0000032.000003320.000000.00000ObjectiveCoefficientAllowableAllowableVariableIncreaseDecreaseE63.0000012.0000015.5000095.0000031.000008.00000D135.0000024.00000InfiniteRHSAllowableAllowableConstraintValueIncreaseDecrease1200.0000080.0000040.000002320.0000080.00000120.0000032400.00000Infinite320.00000The computer solution is shown in Figure 3.17.a. What is the optimal solution, and what is the value of the objective function?b. Which constraints are binding?c. Which constraint shows extra capacity? How much?d. If the profit for the deluxe model were increased to $150 per unit, would the optimalsolution change? Use the information in Figure 3.17 to answer this question.13. Refer to the computer solution of Problem 12 in Figure 3.17.a. Identify the range of optimality for each objective function coefficient.b. Suppose the profit for the economy model is increased by $6 per unit, the profit forthe standard model is decreased by $2 per unit, and the profit for the deluxe model isincreased by $4 per unit. What will the new optimal solution be?c. Identify the range of feasibility for the right-hand-side values.d. If the number of fan motors available for production is increased by 100, will the dualvalue for that constraint change? Explain.

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13. Refer to the computer solution of Problem 12 in Figure 3.17. a. Identify the range of optimality for each objective function coefficient. 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? c. Identify the range of feasibility for the right-hand-side values. d. If the number of fan motors available for production is increased by 100, will the dual value for that constraint change? Explain.