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 Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 240 fan motors, 300 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: Max 63E + 95S + 135D s.t. 1E + 1S + 1D ≤ 240 Fan motors 1E + 2S + 4D ≤ 300 Cooling coils 8E + 12S + 14D ≤ 2,600 Manufacturing time E, S, D ≥ 0 The computer solution is shown below. Optimal Objective Value = 17040.00000 Variable Value Reduced Cost E 180.00000 0.00000 S 60.00000 0.00000 D 0.00000 −24.00000 Constraint Slack/Surplus Dual Value 1 0.00000 31.00000 2 0.00000 32.00000 3 440.00000 0.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease E 63.00000 12.00000 15.50000 S 95.00000 31.00000 8.00000 D 135.00000 24.00000 Infinite Constraint RHS Value Allowable Increase Allowable Decrease 1 240.00000 60.00000 90.00000 2 300.00000 110.00000 60.00000 3 2600.00000 Infinite 440.00000 1. Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) E ______ to ______ S ______ to ______ D ______ to ______ 2. 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? E ______ units S ______ units D ______ units profit $______ 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 ______ to ______ constraint 3 ______ to ______

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 Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 240 fan motors, 300 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: Max 63E + 95S + 135D s.t. 1E + 1S + 1D ≤ 240 Fan motors 1E + 2S + 4D ≤ 300 Cooling coils 8E + 12S + 14D ≤ 2,600 Manufacturing time E, S, D ≥ 0 The computer solution is shown below. Optimal Objective Value = 17040.00000 Variable Value Reduced Cost E 180.00000 0.00000 S 60.00000 0.00000 D 0.00000 −24.00000 Constraint Slack/Surplus Dual Value 1 0.00000 31.00000 2 0.00000 32.00000 3 440.00000 0.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease E 63.00000 12.00000 15.50000 S 95.00000 31.00000 8.00000 D 135.00000 24.00000 Infinite Constraint RHS Value Allowable Increase Allowable Decrease 1 240.00000 60.00000 90.00000 2 300.00000 110.00000 60.00000 3 2600.00000 Infinite 440.00000 1. Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.) E to S to D to 2. 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? E units S units D units profit $ 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 to constraint 3 to

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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Related questions

Question

	Number of Fans	Number of Cooling Coils	Manufacturing Time (hours)
Economy	1	1	8
Standard	1	2	12
Deluxe	1	4	14

For the coming production period, the company has 240 fan motors, 300 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:

Max	63E	+	95S	+	135D
s.t.
	1E	+	1S	+	1D	≤	240	Fan motors
	1E	+	2S	+	4D	≤	300	Cooling coils
	8E	+	12S	+	14D	≤	2,600	Manufacturing time
					E, S, D	≥	0

The computer solution is shown below.

Optimal Objective Value = 17040.00000

Variable	Value	Reduced Cost
E	180.00000	0.00000
S	60.00000	0.00000
D	0.00000	−24.00000

Constraint	Slack/Surplus	Dual Value
1	0.00000	31.00000
2	0.00000	32.00000
3	440.00000	0.00000

Variable	Objective Coefficient	Allowable Increase	Allowable Decrease
E	63.00000	12.00000	15.50000
S	95.00000	31.00000	8.00000
D	135.00000	24.00000	Infinite

Constraint	RHS Value	Allowable Increase	Allowable Decrease
1	240.00000	60.00000	90.00000
2	300.00000	110.00000	60.00000
3	2600.00000	Infinite	440.00000

1. Identify the range of optimality for each objective function coefficient. (If there is no upper or lower limit, enter NO LIMIT.)

E ______ to ______

S ______ to ______

D ______ to ______

2. 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?

E ______ units

S ______ units

D ______ units

profit $______

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 ______ to ______

constraint 3 ______ to ______

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