# Linear Optimization Model

Please assist me in understanding the linear optimization model in the attached document.

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 explain 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.

https://brainmass.com/math/optimization/linear-optimization-model-519257

#### Solution Preview

Dear Student:

The solution for the problem has been presented in the attached Excel worksheet using Excel solver. Please open the Excel file and then continue to read for some clarifying points:

The linear optimization model for total profit ($) = 20.50*small + 34.00*medium + 42.00*large

where small = the number of small air compressors produced, medium = the number of medium air compressors produced, and large = the number of large air compressors produced. The constants in the model are the equivalent unit profits in dollars, as given in the problem.

The model has constraints for production: ...

#### Solution Summary

This solution shows how a linear optimization model can be used to maximize profit for a company that produces three types of air compressors. The company has to take into account both time contraints and production constraints. The solution has been done using Excel solver.