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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 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 23,400Welding 0.6 1.0 1.2 23,400Painting 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.

 

 
   
   
 
         
             
             
  ------- 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  
           

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