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Quality Air Conditioning manufactures three home airconditioners: an economy model, a standard model, and a deluxemodel. 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 fanmotors, 360 cooling coils, and 2600 hours of manufacturing timeavailable. How many economy models (E), standard models (S), anddeluxe models (D) should the company produce in order to maximizeprofit? The linear programming model for the problem is asfollows:

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 functioncoefficient. If there is no limit, then enter the text \"NA\" as youranswer. 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) isincreased by $6 per unit, the profit for the standard model(S) is decreased by $2 per unit, and the profit for thedeluxe model (D) is increased by $4 per unit. What willthe new optimal solution be? If required, round your answers tothree decimal places. If your answer is zero, enter \"0\".
   

   Optimal Solution
   E
   S
   D

   
   If required, round your answer for Total Profit to two decimalplaces.
   
   Total Profit: $_____
   
3. Identify the range of feasibility for the right-hand-sidevalues. If there is no limit, then enter the text \"NA\" as youranswer. 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 isincreased by 60, will the dual value for that constraintchange?
   
   Yes  because the allowable increase for fan motorsis_____without changing the optimal solution.