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
14000
6200
2600

Maximum
21000
12500
4200

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

 

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