1. Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $69, $93, and $131, 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, 380 cooling coils, and 2400 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	+	93S	+	131D
   s.t.
   	1E	+	1S	+	1D		200	Fan motors
   	1E	+	2S	+	4D		380	Cooling coils
   	8E	+	12S	+	14D		2400	Manufacturing time
   E, S, D 0

   The computer solution is shown in the figure below.

   Optimal Objective Value = 18120.00000
   		Variable		Value		Reduced Cost
   		E		20.00000		0.00000
   		S		180.00000		0.00000
   		D		0.00000		-10.00000
   		Constraint		Slack/Surplus		Dual Value
   		1		0.00000		45.00000
   		2		0.00000		24.00000
   		3		80.00000		0.00000

   		Variable		Objective Coefficient		Allowable Increase		Allowable Decrease
   		E		69.00000		5.00000		22.50000
   		S		93.00000		45.00000		3.33333
   		D		131.00000		10.00000		Infinite
   		Constraint		RHS Value		Allowable Increase		Allowable Decrease
   		1		200.00000		20.00000		10.00000
   		2		380.00000		20.00000		180.00000
   		3		2400.00000		Infinite		80.00000

   1. What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nearest whole number. If your answer is zero, enter "0".

      	Optimal Solution
      Economy models (E)	fill in the blank 1
      Standard models (S)	fill in the blank 2
      Deluxe models (D)	fill in the blank 3
      Value of the objective function	$ fill in the blank 4

   2. Which constraints are binding?

      Fan motors:	BindingNon binding
      Cooling coils:	BindingNon binding
      Manufacturing time:	BindingNon binding

   3. Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number.

      Constraints	Extra capacity	Number of units
      Fan motors	YesNo	fill in the blank 9
      Cooling coils	YesNo	fill in the blank 11
      Manufacturing time	YesNo	fill in the blank 13

   4. If the profit for the deluxe model were increased to $146 per unit, would the optimal solution change? The optimal solution

      wouldwould not

      change because the profit of the deluxe model can vary from

      $0$10$121$131$141

      to

      $10$121$131$141infinity

      . $146 is

      innot in

      this range without the optimal solution changing.

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