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Problem: 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:
Available Time
Bending/forming
0.4
0.7
0.8
23,400
Welding
0.6
1.0
1.2
Painting
1.4
2.6
3.1
46,800
How many of each type of air compressor should the company produce to maximize profit?
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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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