Klein Industries manufactures three types of portable air compressors: small m

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 o 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 23400

Welding 0.6 1.0 1.2 23400

Painting 1.4 2.6 3.1 46800

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.