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# Week 7

**Assignment Instructions**

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):**