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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

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.

1. What is the optimal solution, and what is the value of the objective function?

2. Which constraints are binding?

3. Which constraint shows extra capacity? How much?

4. 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 question.

Number of Fans Number of Cooling Coils Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 Max 63E + 955 + 1350 s.t. 1E + 15 + 1D 0 The sensitivity report is shown in Figure 8.18. Figure 8.18. Sensitivity Report for the Quality Air Conditioning Problem Variable Cells Reduced Objective Allowable Allowable Model Variable Name Final Value Cost Coefficient Increase Decrease E Economy Models 80.000 0.000 63.000 12.000 15.500 S Standard Models 120.000 0.000 95.000 31.000 8.000 D Deluxe Models 0.000 -24.000 135.000 24.000 1E+30 Constraints Constraint Shadow Constraint R.H. Allowable Allowable Name Final Value Number Price Side Increase Decrease 1 Fan Motors 200.000 31.000 200.000 80.000 40.000 Cooling Coils 320.000 32.000 320.000 80.000 120.000 N 3 Manufacturing Time 2080.000 0.000 2400.000 1E+30 320.000