Klein Industries manufactures three types of portable air compressors:Solve Problem and Applications: ch 13- prob 7 [Klein Industries manufactures

three types of portable air compressors] in page 451 at the end of chapter 13

in your textbook, USA 5th edition. The data is given as part of the question.

There is no external data set provided. Use what is given by the problem.

13-7. 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:

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 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.