Problem 3-12
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, respectively. The production requirements per unit are
as follows:
Number of Number of Manufacturing
Fans Cooling Coils Time (hours)
Economy 1 1 8
Standard 1 2 12
Deluxe 1 4 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 + 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 the figure below.
Optimal Objective Value = 16440.00000
Variable Value Reduced Cost
E 80.00000 0.00000
S 120.00000 0.00000
D 0.00000 -24.00000
Constraint Slack/Surplus Dual Value
1 0.00000 31.00000
2 0.00000 32.00000
3 320.00000 0.00000
Objective Allowable Allowable
Variable
Coefficient Increase Decrease
This study source was downloaded by 100000827161609 from CourseHero.com on 04-26-2023 01:13:42 GMT -05:00
https://www.coursehero.com/file/89915626/lps2pdf/
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:
Number of Number of Manufacturing
Fans Cooling Coils Time (hours)
Economy 1 1 8
Standard 1 2 12
Deluxe 1 4 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 + 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 the figure below.
Optimal Objective Value = 16440.00000
Variable Value Reduced Cost
E 80.00000 0.00000
S 120.00000 0.00000
D 0.00000 -24.00000
Constraint Slack/Surplus Dual Value
1 0.00000 31.00000
2 0.00000 32.00000
3 320.00000 0.00000
Objective Allowable Allowable
Variable
Coefficient Increase Decrease
This study source was downloaded by 100000827161609 from CourseHero.com on 04-26-2023 01:13:42 GMT -05:00
https://www.coursehero.com/file/89915626/lps2pdf/
