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,

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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:

Max 63E + 95S + 135D

s.t.

1E + 1S + 1D ‰¤ 200 Fan motors

1E + 2S 4D ‰¤ 320 Cooling coils

8E + 12S + 14D ‰¤ 2400 Manufacturing time

E, S, D ‰¥ 0

The 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 optimal solution change? Use the information in Figure 3.17 to answer this question.

Number of Fans 1 Number of Cooling Coils Manufacturing Time (hours) Economy 12 14 Standard Deluxe 1 4 Optimal Objective Value = 16440.00000 Variable Value Reduced Cost 80.00000 0.00000 120.00000 0.00000 D 0.00000 -24.00000 Constraint Slack/Surplus Dual Value 1. 0.00000 31.00000 0.00000 32.00000 320.00000 0.00000 Objective Allowable Allowable Variable Coefficient Increase Decrease 63.00000 12.00000 15.50000 95.00000 31.00000 8.00000 D 135.00000 24.00000 Infinite RHS Allowable Allowable Constraint Value Increase Decrease 200.00000 80.00000 40.00000 320.00000 80.00000 120.00000 2400.00000 Infinite 320.00000