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12. 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, respec- tively. The production requirements per unit are as follows: Number of Fans 1 1 1 Number of Cooling Coils 1 2 Manufacturing Time (hours) 8 Economy Standard Deluxe 12 14 For 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), 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 +955 + 1350 s.t. 1E + IS+ IDS 200 Fan motors 1E + 25 + 4D S 320 Cooling coils 8E + 125 + 14D = 2400 Manufacturing time E,S,D 20 342 Chapter 8 Linear Programming: Sensitivity Analysis and Interpretation of Solution FIGURE 8.18 SENSITIVITY REPORT FOR THE QUALITY AIR CONDITIONING PROBLEM Variable Cells Model Variable E S D Name Economy Models Standard Models Deluxe Models Final Value 80.000 120.000 0.000 Reduced Cost 0.000 0.000 - 24.000 Objective Coefficient 63.000 95.000 135.000 Allowable Increase 12.000 31.000 24.000 Allowable Decrease 15.500 8.000 1E+30 Constraints Constraint Number 1 2 3 Name Fan Motors Cooling Coils Manufacturing Time Final Value 200.000 320.000 2080.000 Shadow Price 31.000 32.000 0.000 Constraint R.H. Side 200.000 320.000 2400.000 Allowable Increase 80.000 80.000 1E+30 Allowable Decrease 40.000 120.000 320.000 The sensitivity report is shown in Figure 8.18. 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 optimal solution change? Use the information in Figure 8.18 to answer this