Question

Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $61, $99, 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 250 fan motors, 360 cooling coils, and 2600 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	61E	+	99S	+	135D
s.t.
	1E	+	1S	+	1D	≤	250	Fan motors
	1E	+	2S	+	4D	≤	360	Cooling coils
	8E	+	12S	+	14D	≤	2600	Manufacturing time
E, S, D ≥ 0

The sensitivity report is shown in the figure below.

Optimal Objective Value =      19430.00000
		Variable		Value		Reduced Cost
		E		140.00000		0.00000
		S		110.00000		0.00000
		D		0.00000		40.00000
		Constraint		Slack/Surplus		Dual Value
		Fan motors		0.00000		23.00000
		Cooling coils		0.00000		38.00000
		Manufacturing time		160.00000		0.00000

		Variable		Objective Coefficient		Allowable Increase		Allowable Decrease
		E		61.00000		20.00000		11.50000
		S		99.00000		23.00000		13.33333
		D		135.00000		40.00000		Infinite
		Constraint		RHS Value		Allowable Increase		Allowable Decrease
		Fan motors		250.00000		40.00000		70.00000
		Cooling coils		360.00000		40.00000		110.00000
		Manufacturing time		2600.00000		Infinite		160.00000

1. Identify the range of optimality for each objective function coefficient. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
   

   	Objective Coefficient Range
   Variable	lower limit	upper limit
   E
   S
   D

2. Suppose the profit for the economy model (E) is increased by $6 per unit, the profit for the standard model (S) is decreased by $2 per unit, and the profit for the deluxe model (D) is increased by $4 per unit. What will the new optimal solution be? If required, round your answers to three decimal places. If your answer is zero, enter "0".
   

   Optimal Solution
   E
   S
   D

   
   If required, round your answer for Total Profit to two decimal places.
   
   Total Profit: $_____
   
3. Identify the range of feasibility for the right-hand-side values. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
   

   	Right-Hand-Side-Range
   Constraints	lower limit	upper limit
   Fan motors
   Cooling coils
   Manufacturing time

4. If the number of fan motors available for production is increased by 60, will the dual value for that constraint change?
   
   Yes  because the allowable increase for fan motors is_____without changing the optimal solution.

Answer 1