Question

Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $69, $91, and $127, 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 200 fan motors, 340 cooling coils, and 2800 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	69E	+	91S	+	127D
s.t.
	1E	+	1S	+	1D	≤	200	Fan motors
	1E	+	2S	+	4D	≤	340	Cooling coils
	8E	+	12S	+	14D	≤	2800	Manufacturing time
E, S, D ≥ 0

The sensitivity report is shown in the figure below.

Optimal Objective Value =      16880.00000
		Variable		Value		Reduced Cost
		E		60.00000		0.00000
		S		140.00000		0.00000
		D		0.00000		8.00000
		Constraint		Slack/Surplus		Dual Value
		Fan motors		0.00000		47.00000
		Cooling coils		0.00000		22.00000
		Manufacturing time		640.00000		0.00000

		Variable		Objective Coefficient		Allowable Increase		Allowable Decrease
		E		69.00000		4.00000		23.50000
		S		91.00000		47.00000		2.66667
		D		127.00000		8.00000		Infinite
		Constraint		RHS Value		Allowable Increase		Allowable Decrease
		Fan motors		200.00000		140.00000		30.00000
		Cooling coils		340.00000		60.00000		140.00000
		Manufacturing time		2800.00000		Infinite		640.00000

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 160, will the dual value for that constraint change?
   
     because the allowable increase for fan motors is  without changing the optimal solution.

Answer 1