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.

P