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 using The Management Scientist is shown in Figure.
THE MANAGEMENT SCIENTIST SOLUTION FOR THE QUALITY AIR CONDITIONING PROBLEM

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 8.19 to answer thisquestion.

Transcribed Image Text:

Number of Fans Number of Cooling Coils Manufacturing Time (hours) Economy Standard Deluxe 12 14 4 Objective Function Value - 16440.000 Variable Value Reduced Costs 80.000 120.000 0.000 0.000 0.000 24.000 Constraint Slack/Surplus Dual Prices 0.000 0.000 320.000 31.000 32.000 0.000 OBJECTIVE COEEFICIENT RANGES Variable Lower Limit Current Value Upper Limit 47.500 87.000 No Lower Limit 63.000 95.000 135.000 75.000 126.000 159.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 160 000 200 000 2080.000 200.000 320.000 2400.000 280.000 400.000 No Upper Linit