13-7. Klein Industries manufactures three types of portableair
compressors: small, medium, and large, which haveunit 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 23,400Welding 0.6 1.0 1.2
23,400Painting 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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| ------- Slip Ring ------- | |||||||||||
| Number to | Model 1 | Model 2 | Model 3 | ||||||||
| Make | 0 | 0 | 0 | ||||||||
| Buy | 0 | 0 | 0 | ||||||||
| Cost to | |||||||||||
| Make | $50 | $83 | $130 | Total Cost | |||||||
| Buy | $61 | $97 | $145 | $0 | |||||||
| # Available | 0 | 0 | 0 | ||||||||
| # Needed | 3,000 | 2,000 | 900 | ||||||||
| Hours Required | Used | Available | |||||||||
| Wiring | 2 | 1.5 | 3 | 0 | 10,000 | ||||||
| Harnessing | 1 | 2 | 1 | 0 | 5,000 | ||||||
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