# Linear Optimization Model Problem

I need quick help with this problem and Excel SOLVER setup. I would like someone to review this, fix the solver issues and explain this problems outcome.

Linear Optimization Model: 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. Additional Slides 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.

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#### Solution Preview

(the following text is also attached as "Hello Student.doc")

Hello Student,

I reviewed this.

Your attachment "Week 7 519257 Klein Industries.xlsx" is done in Solver and has Excel SOLVER figures. See my attachment solver.jpg. I went to Data tab, then Solver and opened up the constraints set up. If you mean something different by "SOLVER figures", let me know.

To explain this problems outcome, see my attachment Klein.xls. This is a copy of your aforementioned spreadsheet attachment with the first tab duplicated at the end as "Sheet ...

#### Solution Summary

Excel SOLVER setup screenshot in a jpg file.

Explanation is in an xls file as an annotated version of the submitted problem.

This includes explanation of the Sensitivity Report.