Problem and Applications

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 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. Be sure to review links provided in the last lesson, or in one of the announcements in the first week of class. Here is a You Tube link you could view: http://www.youtube.com/watch?v=Oyc0k9kiD7o 
Also additional slides to explain basics 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.

Turn It In (TII):
TII is integrated in this course which means you will not need your own account for submitting papers.  Your faculty member will decide for each assignment if your paper needs to be submitted to TII.  Please submit each assignment only in the Assignments area.
here’s supporting material
     
     
     
  ——- Slip Ring ——-    
Number to Model 1 Model 2 Model 3  
    Make     0  0  0   
    Buy 0  0  0   
     
Cost to     
    Make     $50  $83  $130  Total Cost 
    Buy $61  $97  $145  $0  
     
# Available 0  0  0   
# Needed 3,000  2,000  900   
     
Hours Required     Used Available
    Wiring 2  1.5  3  0  10,000
    Harnessing 1  2  1  0  5,000
Content and Organization  Points Available Points Earned Comments
Assignment details and requirements and elements. : The content is comprehensive, accurate, and/or persuasive. Results interpreted and conclusions delivered. Excel work, if required, is an original sheet with the all details of work and calculations included. 80    
  80 0  
Readability and Style  Points Available Points Earned Comments
Content is present, logical and maintain the flow throughout the answers 10    
Work is identified and organized 10    
  20    
Late penalty   0  
Final Score 100 0  
Total  100 0
 

 
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