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 2,500 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		220	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 = 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	180.00000	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	45.00000	40.00000
2	360.00000	45.00000	140.00000
3	2500.00000	Infinite	180.00000

(a)

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

(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?

E unitsS unitsD unitsprofit$

(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

to

constraint 3

to

(d)

If the number of fan motors available for production is increased by 75, will the dual value for that constraint change? Explain.

Yes, the dual value will change because 75 is greater than the allowable increase of 45.Yes, the dual value will change because 75 is greater than the allowable increase of 12. No, the dual value will not change because there is no upper limit to how much the constraint can increase.No, the dual value will not change because 75 is less than the allowable increase of 265.