Question

1. 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 sensitivity report 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
   		Fan motors		80.00000		0.00000
   		Cooling coils		0.00000		7.00000
   		Manufacturing time		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
   		Fan motors		300.00000		Infinite		80.00000
   		Cooling coils		340.00000		231.42860		90.00000
   		Manufacturing time		2000.00000		480.00000		810.00000

   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 manufacturing time available for production is increased by 500, will the dual value for that constraint change?
      
      
      • Yes
      • No
      because the allowable increase for manufacturing time is without changing the optimal solution.

Answer 1