Problem 3-13 (Algorithmic)

Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $93, and $129, 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 1800 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	67 E	+	93 S	+	129 D
s.t.
	1E	+	1S	+	1D		250	Fan motors
	1E	+	2S	+	4D		360	Cooling coils
	8E	+	12S	+	14D		1800	Manufacturing time
E, S, D 0

The sensitivity report is shown in the figure below.

Optimal Objective Value = 15780.00000
		Variable		Value		Reduced Cost
		E		120.00000		0.00000
		S		0.00000		10.11111
		D		60.00000		0.00000
		Constraint		Slack/Surplus		Dual Value
		Fan motors		70.00000		0.00000
		Cooling coils		0.00000		5.22222
		Manufacturing time		0.00000		7.72222

		Variable		Objective Coefficient		Allowable Increase		Allowable Decrease
		E		67.00000		6.71429		9.10000
		S		93.00000		10.11111		Infinite
		D		129.00000		139.00000		11.75000
		Constraint		RHS Value		Allowable Increase		Allowable Decrease
		Fan motors		250.00000		Infinite		70.00000
		Cooling coils		360.00000		154.28570		135.00000
		Manufacturing time		1800.00000		420.00000		540.00000

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	fill in the blank 1	fill in the blank 2
   S	fill in the blank 3	fill in the blank 4
   D	fill in the blank 5	fill in the blank 6

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	fill in the blank 7
   S	fill in the blank 8
   D	fill in the blank 9

   If required, round your answer for Total Profit to two decimal places. Total Profit: $ fill in the blank 10
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	fill in the blank 11	fill in the blank 12
   Cooling coils	fill in the blank 13	fill in the blank 14
   Manufacturing time	fill in the blank 15	fill in the blank 16

4. If the number of manufacturing time available for production is increased by 440, will the dual value for that constraint change? because the allowable increase for manufacturing time is fill in the blank 18 without changing the optimal solution.