# Optimization

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 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. Here is a You Tube link you could view: http://www.youtube.com/watch?v=Oyc0k9kiD7o
I HAVE ATTACHED A SAMPLE SOLUTION OF SOLVER TITLED. SOLVER.XLSX, CROSS CHECK YOUR SOLUTION WITH THIS SOLUTION TO GIVE YOU AN IDEA OF WHAT IS REQUIRED. DON’T FORGET THE FIRST QUSTION ASKS YOU TO WRITE A SHORT MEMO AFTER SOLVING QUESTION A THEN AFTER SOLVING QUESTION B.
ABSOLUTELY NO PLAGIARISM.

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