Reference no: EM132497589

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
 
Question 1: How many of each type of air compressor should the company produce to maximize profit?

Question 2: 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.

Question 3: Solve the model without the auxiliary variables and explain the relationship between the reduced costs and the shadow prices found in Question 2.