Klein Industries manufactures three types of portable air compressors: small, medium and large, which have units 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 2

Klein Industries manufactures three types of portable  air compressors: small, medium and large, which have units 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 variables cells methods 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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