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 $135, respectively. The production requirements per unit are as follows: Number of Fans Number of Cooling Coils Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 220 fan motors, 340 cooling coils, and 2,600 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 63E + 95S + 135D s.t. 1E + 1S + 1D ≤ 220 Fan motors 1E + 2S + 4D ≤ 340 Cooling coils 8E + 12S + 14D ≤ 2,600 Manufacturing time E, S, D ≥ 0 The computer solution is shown below. Optimal Objective Value = 17700.00000 Variable Value Reduced Cost E 100.00000 0.00000 S 120.00000 0.00000 D 0.00000 24.00000 Constraint Slack/Surplus Dual Value 1 0.00000 31.00000 2 0.00000 32.00000 3 360.00000 0.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease E 63.00000 12.00000 15.50000 S 95.00000 31.00000 8.00000 D 135.00000 24.00000 Infinite Constraint RHS Value Allowable Increase Allowable Decrease 1 220.00000 90.00000 50.00000 2 340.00000 90.00000 120.00000 3 2600.00000 Infinite 360.00000 (a) What is the optimal solution, and what is the value of the objective function? ESDprofit$ (b) Which constraints are binding? (Select all that apply.) fan motorscooling coilsmanufacturing time (c) Which constraint shows extra capacity? fan motorscooling coils manufacturing time How much extra capacity (in hr) is available? hr (d) If the profit for the deluxe model were increased to $145 per unit, would the optimal solution change? Use the information in the output to answer this question. The optimal solution change because the new profit is the .

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 $135, respectively. The production requirements per unit are as follows: Number of Fans Number of Cooling Coils Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 220 fan motors, 340 cooling coils, and 2,600 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 63E + 95S + 135D s.t. 1E + 1S + 1D ≤ 220 Fan motors 1E + 2S + 4D ≤ 340 Cooling coils 8E + 12S + 14D ≤ 2,600 Manufacturing time E, S, D ≥ 0 The computer solution is shown below. Optimal Objective Value = 17700.00000 Variable Value Reduced Cost E 100.00000 0.00000 S 120.00000 0.00000 D 0.00000 24.00000 Constraint Slack/Surplus Dual Value 1 0.00000 31.00000 2 0.00000 32.00000 3 360.00000 0.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease E 63.00000 12.00000 15.50000 S 95.00000 31.00000 8.00000 D 135.00000 24.00000 Infinite Constraint RHS Value Allowable Increase Allowable Decrease 1 220.00000 90.00000 50.00000 2 340.00000 90.00000 120.00000 3 2600.00000 Infinite 360.00000 (a) What is the optimal solution, and what is the value of the objective function? ESDprofit$ (b) Which constraints are binding? (Select all that apply.) fan motorscooling coilsmanufacturing time (c) Which constraint shows extra capacity? fan motorscooling coils manufacturing time How much extra capacity (in hr) is available? hr (d) If the profit for the deluxe model were increased to $145 per unit, would the optimal solution change? Use the information in the output to answer this question. The optimal solution change because the new profit is the .

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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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 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:

Max	63E	+	95S	+	135D
s.t.
	1E	+	1S	+	1D	≤	220	Fan motors
	1E	+	2S	+	4D	≤	340	Cooling coils
	8E	+	12S	+	14D	≤	2,600	Manufacturing time
					E, S, D	≥	0

The computer solution is shown below.

Optimal Objective Value = 17700.00000

Variable	Value	Reduced Cost
E	100.00000	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	360.00000	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	220.00000	90.00000	50.00000
2	340.00000	90.00000	120.00000
3	2600.00000	Infinite	360.00000

(a)

What is the optimal solution, and what is the value of the objective function?

ESDprofit$

(b)

Which constraints are binding? (Select all that apply.)

fan motorscooling coilsmanufacturing time

(c)

Which constraint shows extra capacity?

fan motorscooling coils manufacturing time

How much extra capacity (in hr) is available?

(d)

If the profit for the deluxe model were increased to $145 per unit, would the optimal solution change? Use the information in the output to answer this question.

The optimal solution change because the new profit is the .

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