12. a-d and 13. a-d

12. Quality Air Conditioning manufactures three home air conditioners: an cconomy model a standard model, and a deluxe model. The profits per unit are S63-995, and $135, np tively. The production requirements per unit are as follows Number of Fans Number of Cooling Cods Manufacturing Time hours Standard Deluxe 12 14 For the coming production period, the company has 200 fan motons, 320 cooling coils and 2400 hours of manufacturing time available. How many ecconomy models (E), sts dard models (S), and deluxe models (D) should the company produce in oeder to maximie profit? The linear programming model for the problem is as follows Max 63E955+135D 1S+Ds 200 Fan motors E+25 4Ds 320 Cooling coils E+12514D 2400 Manfacturing time FIGURE 3.17 THE SOLUTION FOR THE QUALITY AIR CONDTIONING PROBLEM Optimal objective Value 16440.00000 Reduced Cost 80.00000 120.00000 0.00000 -24.00000 Dual Value 2.00000 abjective Variable Coeffielent 63.00000 135.00000 12.00000 24.0000O Allowable 15.50000 Intinice Allovable 200.00000 20.00000 2400.0b000 80.00000 40.00000 Infinite 20.00000 The computer solution is shown in Figure 3.17. h Which constraints are binding? d. If the profit for the deluxe model were increased to $150 per unit, would the ogtima What is the optimal solution, and what is the value of the otjective function? Which constraint shows extra capacity? How much? solution change? Use the informatioe in Figure 317 so 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 ooefficient h Suppose the profit for the economy model is increased by $6 per unit, the proit for the standard model is decreased by $2 per unit, and the profit for the deluse model is increased by 34 per unit. What will the new optimal solution be? e. Identify the range of feasibility for the right-hand-side valucs d. If the number of fan motors available for prodaction is increased by 100, wil the dua valac for that constraint change? Explain