# Problem and Applications

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.

Solution Tip: You must use Solver tool in Excel. Set your constraints right, and fill in the solver dialogue box properly. Be sure to review links provided in the last lesson, or in one of the announcements in the first week of class. Here is a You Tube link you could view: http://www.youtube.com/watch?v=Oyc0k9kiD7o
Also additional slides to explain basics and a basic example is attached. The example and slides are for demonstration and illustration purpose only to help practice how to use solver tool.

Turn It In (TII):
TII is integrated in this course which means you will not need your own account for submitting papers.  Your faculty member will decide for each assignment if your paper needs to be submitted to TII.  Please submit each assignment only in the Assignments area.
here’s supporting material

——- Slip Ring ——-
Number to Model 1 Model 2 Model 3
Make     0  0  0
Buy 0  0  0

Cost to
Make     \$50  \$83  \$130  Total Cost
Buy \$61  \$97  \$145  \$0

# Available 0  0  0
# Needed 3,000  2,000  900

Hours Required     Used Available
Wiring 2  1.5  3  0  10,000
Harnessing 1  2  1  0  5,000
 Content and Organization Points Available Points Earned Comments Assignment details and requirements and elements. : The content is comprehensive, accurate, and/or persuasive. Results interpreted and conclusions delivered. Excel work, if required, is an original sheet with the all details of work and calculations included. 80 80 0 Readability and Style Points Available Points Earned Comments Content is present, logical and maintain the flow throughout the answers 10 Work is identified and organized 10 20 Late penalty 0 Final Score 100 0 Total 100 0