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 Fans Number of Cooling Coils Economy Standard. Deluxe Max s.t. 1 Variable E $ D 1 1E + 15 + 1E + 25 + 8E+12S + Constraint 1 2 3 1 Variable E S The computer solution is shown below. Optimal Objective Value Value 100.00000 120.00000 0.00000 For the coming production period, the company has 220 fan motors, 340 cooling coils, and 2,600 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce. profit? The linear programming model for the problem is as follows: 63E + 95S + 135D 1 2 Slack/Surplus 4 0.00000 0.00000 360.00000 63.00000 95.00000 1D S 220 4D S 340 14D 2,600 Manufacturing time E, S, D 20 17700.00000 Manufacturing Time (hours) Reduced Cost 0.00000 0.00000 -24.00000 8 12 14 Fan motors Cooling coils Dual Value 31.00000 32.00000 0.00000 Objective Allowable Allowable Coefficient Increase Decrease 12.00000 31.00000 15.50000 8.00000 order to maximize

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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:
Number of
Cooling Coils
Economy
Standard
Deluxe
Max
s.t.
63E+ 95S +
Variable
E
S
D
Number of
Fans
Constraint
1
2
3
Variable
1
E
-
1
1E + 1S +
1E + 2S +
8E+12S +
S
1
For the coming production period, the company has 220 fan motors, 340 cooling coils, and 2,600 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:
The computer solution is shown below.
D
135D
Optimal Objective Value = 17700.00000
E, S, D 20
1D ≤ 220
4D ≤ 340
14D 2,600
1
Value
100.00000
120.00000
0.00000
2
4
Slack/Surplus
0.00000
0.00000
360.00000
Reduced Cost
0.00000
0.00000
-24.00000
Manufacturing
Time (hours)
8
12
Fan motors
Cooling coils
Manufacturing time
Dual Value
31.00000
32.00000
0.00000
14
Objective Allowable Allowable
Coefficient
Increase
Decrease
12.00000
15.50000
63.00000
95.00000
135.00000
31.00000
8.00000
24.00000
Infinite
Transcribed Image Text: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 Cooling Coils Economy Standard Deluxe Max s.t. 63E+ 95S + Variable E S D Number of Fans Constraint 1 2 3 Variable 1 E - 1 1E + 1S + 1E + 2S + 8E+12S + S 1 For the coming production period, the company has 220 fan motors, 340 cooling coils, and 2,600 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: The computer solution is shown below. D 135D Optimal Objective Value = 17700.00000 E, S, D 20 1D ≤ 220 4D ≤ 340 14D 2,600 1 Value 100.00000 120.00000 0.00000 2 4 Slack/Surplus 0.00000 0.00000 360.00000 Reduced Cost 0.00000 0.00000 -24.00000 Manufacturing Time (hours) 8 12 Fan motors Cooling coils Manufacturing time Dual Value 31.00000 32.00000 0.00000 14 Objective Allowable Allowable Coefficient Increase Decrease 12.00000 15.50000 63.00000 95.00000 135.00000 31.00000 8.00000 24.00000 Infinite
E
S
D
ESA
E
S
D
Constraint
Allowable
Increase
90.00000
Allowable
Decrease
50.00000
90.00000 120.00000
Infinite 360.00000
(a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.)
profit $
1
2
63.00000
95.00000
135.00000
3
RHS
Value
220.00000
340.00000
2600.00000
to
to
to
12.00000
31.00000
24.00000
(b) Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be?
units
units
units
15.50000
8.00000
Infinite
to
to
(c) Identify the range of feasibility for the right-hand-side values. (If there is no upper or lower limit, enter NO LIMIT.)
constraint 1
to
constraint 2
constraint 3
Transcribed Image Text:E S D ESA E S D Constraint Allowable Increase 90.00000 Allowable Decrease 50.00000 90.00000 120.00000 Infinite 360.00000 (a) Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) profit $ 1 2 63.00000 95.00000 135.00000 3 RHS Value 220.00000 340.00000 2600.00000 to to to 12.00000 31.00000 24.00000 (b) Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be? units units units 15.50000 8.00000 Infinite to to (c) Identify the range of feasibility for the right-hand-side values. (If there is no upper or lower limit, enter NO LIMIT.) constraint 1 to constraint 2 constraint 3
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