# How many of each type of air compressor should the company produce to maximize profit?

###### How many of each type of air compressor should the company produce to maximize profit?
Words: 234
Pages: 1
Subject: Accounting

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.

Tags