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 portableair compressors: small medium and large which haveunit profits of $20.50 $34.00 and $42.00 respectively.The projected monthly sales are:
Small Medium Large
Minimum 14000 6200 2600
Maximum 21000 12500 4200
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 23400
Welding 0.6 1.0 1.2 23400
Painting 1.4 2.6 3.1 46800
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.