Assignment Prompt:

SolveProblem 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.You need to submit a formal APA paper to explain all your findings together with your Excel Worksheet to demonstrate you have set up the Solver correctly. In the paper, you also need to explain how you set up the LP model to solve this case study.

13-7.Klein Industries manufactures three types of portableair compressors: small, medium, and large, which haveunit profits of $20.50, $34.00, and $42.00, respectively.The projected monthly sales are:

SmallMediumLarge

Minimum14,0006,2002,600

Maximum21,00012,5004,200

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:

SmallMediumLargeAvailable Time

Bending/forming0.40.70.823,400

Welding0.61.01.223,400

Painting1.42.63.146,800

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 create 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.