[solved]-Problem 3 13 Algorithmic Quality Air Conditioning Manufactures Three Home Air Conditioners Q39669231

Problem 3-13 (Algorithmic)

Quality Air Conditioning manufactures three home airconditioners: an economy model, a standard model, and a deluxemodel. The profits per unit are $59, $89, and $137, respectively.The production requirements per unit are as follows:

Number of
FansNumber of
Cooling CoilsManufacturing
Time (hours)Economy118Standard1212Deluxe1414

For the coming production period, the company has 240 fanmotors, 380 cooling coils, and 2500 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:

Max59E+89S+137Ds.t.1E+1S+1D≤240  Fan motors1E+2S+4D≤380  Cooling coils8E+12S+14D≤2500  Manufacturing timeE, S, D ≥ 0

The sensitivity report is shown in the figure below.

Optimal Objective Value=      18360.00000VariableValueReduced CostE100.000000.00000S140.000000.00000D0.0000012.00000ConstraintSlack/SurplusDual ValueFan motors0.0000029.00000Cooling coils0.0000030.00000Manufacturing time20.000000.00000VariableObjective
CoefficientAllowable
IncreaseAllowable
DecreaseE59.000006.0000014.50000S89.0000029.000004.00000D137.0000012.00000InfiniteConstraintRHS
ValueAllowable
IncreaseAllowable
DecreaseFan motors240.000005.0000050.00000Cooling coils380.000005.00000140.00000Manufacturing time2500.00000Infinite20.00000

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 RangeVariablelower limitupper limitESD
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 SolutionESD
   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-RangeConstraintslower limitupper limitFan motorsCooling coilsManufacturing time
4. If the number of cooling coils available for production isincreased by 25, will the dual value for that constraintchange?

   Yes  because the allowable increase for cooling coilsis  without changing the optimal solution.

Expert Answer

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Answer to Problem 3-13 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standa… . . .