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 $135, respectively The production requirements per unit are as follows Number of Fans Number of Cooling Coils Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 220 fan motors, 360 cooling coils, and 2,600 hours of manufacturing time available How many economy models ( E ), standard models ( S ), and deluxe models ( D ) should the company produce in order to maximize profit The linear programming model for the problem is as follows Max 63 E 95 S 135 D s t 1 E 1 S 1 D 220 Fan motors 1 E 2 S 4 D 360 Cooling coils 8 E 12 S 14 D 2,600 Manufacturing time E , S , D 0 The computer solution is shown below Optimal Objective Value 18340 00000 Variable Value Reduced Cost E 80 00000 0 00000 S 140 00000 0 00000 D 0 00000 24 00000 Constraint Slack Surplus Dual Value 1 0 00000 31 00000 2 0 00000 32 00000 3 280 00000 0 00000 Variable Objective Coefficient Allowable Increase Allowable Decrease E 63 00000 12 00000 15 50000 S 95 00000 31 00000 8 00000 D 135 00000 24 00000 Infinite Constraint RHS Value Allowable Increase Allowable Decrease 1 220 00000 70 00000 40 00000 2 360 00000 70 00000 140 00000 3 2600 00000 Infinite 280 00000 (a) What is the optimal solution, and what is the value of the objective function E S D profit$ (b) Which constraints are binding (Select all that apply ) fan motors cooling coils manufacturing time (c) Which constraint shows extra capacity fan motors cooling 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 Select would not change because the new profit is Select within outside the Select range of feasibility range of optimality

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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,

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, 360 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	360	Cooling coils
	8E	+	12S	+	14D	2,600	Manufacturing time
					E, S, D	0

The computer solution is shown below.

Optimal Objective Value = 18340.00000

Variable	Value	Reduced Cost
E	80.00000	0.00000
S	140.00000	0.00000
D	0.00000	24.00000

Constraint	Slack/Surplus	Dual Value
1	0.00000	31.00000
2	0.00000	32.00000
3	280.00000	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	70.00000	40.00000
2	360.00000	70.00000	140.00000
3	2600.00000	Infinite	280.00000

(a)

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

profit$

(b)

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

fan motors

cooling coils

manufacturing time

(c)

Which constraint shows extra capacity?

fan motors

cooling 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 ---Select--- would not change because the new profit is ---Select--- within outside the ---Select--- range of feasibility range of optimality.