Question

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 $57, $93, and $141, 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 320 fan motors, 380 cooling coils, and 3200 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	57E	+	93S	+	141D
s.t.
	1E	+	1S	+	1D	≤	320	Fan motors
	1E	+	2S	+	4D	≤	380	Cooling coils
	8E	+	12S	+	14D	≤	3200	Manufacturing time
E, S, D ≥ 0

The computer solution is shown in the figure below.

Optimal Objective Value =      20400.00000
		Variable		Value		Reduced Cost
		E		260.00000		0.00000
		S		60.00000		0.00000
		D		0.00000		24.00000
		Constraint		Slack/Surplus		Dual Value
		1		0.00000		21.00000
		2		0.00000		36.00000
		3		400.00000		0.00000

		Variable		Objective Coefficient		Allowable Increase		Allowable Decrease
		E		57.00000		12.00000		10.50000
		S		93.00000		21.00000		8.00000
		D		141.00000		24.00000		Infinite
		Constraint		RHS Value		Allowable Increase		Allowable Decrease
		1		320.00000		60.00000		130.00000
		2		380.00000		100.00000		60.00000
		3		3200.00000		Infinite		400.00000

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:
   Cooling coils:
   Manufacturing time:

3. 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
   Cooling coils
   Manufacturing time

4. If the profit for the deluxe model were increased to $156 per unit, would the optimal solution change?
   
   The optimal solution   change because the profit of the deluxe model can vary from   to  . $156 is   this range without the optimal solution changing.

Answer 1