Question

In: Statistics and Probability

Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a...

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.

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