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 260 fan motors, 360 cooling coils, and 2,500 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		260	Fan motors
	1E	+	2S	+	4D		360	Cooling coils
	8E	+	12S	+	14D		2,500	Manufacturing time
					E, S, D		0

The computer solution is shown below.

Optimal Objective Value = 19580.00000

Variable	Value	Reduced Cost
E	160.00000	0.00000
S	100.00000	0.00000
D	0.00000	24.00000

Constraint	Slack/Surplus	Dual Value
1	0.00000	31.00000
2	0.00000	32.00000
3	20.00000	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	260.00000	5.00000	80.00000
2	360.00000	5.00000	100.00000
3	2500.00000	Infinite	20.00000

(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 ___________change because the new profit is________the_______.