Klein Industries Optimization Model

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Klein Industries Optimization Model
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APA paper to explain all your findings together with your Excel Worksheet to demonstrate you have set up the Solver correctly. In the paper, you also need to explain how you set up the LP model to solve this case study.
Klein Industries manufactures three types of portable air compressors: small, medium, and large, which have unit profits of $20.50, $34.00, and $42.00, respectively. The projected monthly sales are:
                 Small     Medium  Large 
Minimum  14,000   6,200      2,600 
Maximum  21,000  12,500    4,200
The production process consists of three primary activities: bending and forming, welding, and painting. The amount of time in minutes needed to process each product in each department is shown below: 
                                Small  Medium  Large  Available Time  
Bending/forming          0.4       0.7       0.8       23,400 
Welding                       0.6       1.0       1.2       23,400 
Painting                       1.4       2.6       3.1       46,800 

How many of each type of air compressor should the company produce to maximize profit? 
a. Formulate and solve a linear optimization model using the auxiliary variable cells method and write a short memo to the production manager explaining the sensitivity information. 

b.  Solve the model without the auxiliary variables and explain the relationship between the reduced costs and the shadow prices found in part a. 


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