Problem 3-12 (Algorithmic)

Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $95, and $133, 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 300 fan motors, 340 cooling coils, and 2000 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	67E	+	95S	+	133D
s.t.
	1E	+	1S	+	1D		300	Fan motors
	1E	+	2S	+	4D		340	Cooling coils
	8E	+	12S	+	14D		2000	Manufacturing time
E, S, D 0

The computer solution is shown in the figure below.

Optimal Objective Value =17380.00000
		Variable		Value		Reduced Cost
		E		180.00000		0.00000
		S		0.00000		9.00000
		D		40.00000		0.00000
		Constraint		Slack/Surplus		Dual Value
		1		80.00000		0.00000
		2		0.00000		7.00000
		3		0.00000		7.50000

		Variable		Objective Coefficient		Allowable Increase		Allowable Decrease
		E		67.00000		9.00000		8.10000
		S		95.00000		9.00000		Infinite
		D		133.00000		135.00000		15.75000
		Constraint		RHS Value		Allowable Increase		Allowable Decrease
		1		300.00000		Infinite		80.00000
		2		340.00000		231.42860		90.00000
		3		2000.00000		480.00000		810.00000

1. What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nearest whole number. If your answer is zero, enter "0".

	Optimal Solution
Economy models (E)	?
Standard models (S)	?
Deluxe models (D)	?
Value of the objective function	$___?___

2. Which constraints are binding?

Fan motors:	Binding or Non binding?
Cooling coils:	Binding or Non binding?
Manufacturing time:	Binding or Non binding?

2. Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number.

Constraints	Extra capacity	Number of units
Fan motors	Yes or No?	?
Cooling coils	Yes or No?	?
Manufacturing time	Yes or No?	?

1. If the profit for the standard model were increased to $110 per unit, would the optimal solution change?
2. The optimal solution (would or would not) change because the profit of the standard model can vary from ($0, $9, $86, $95, $104) to ($9, $86, $95, $104, Infinity). $110 is (in or not in) this range without the optimal solution changing.