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:

SmallMediumLarge

Minimum14,0006,2002,600

Maximum21,00012,5004,200

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:

SmallMediumLargeAvailable Time

Bending/forming0.40.70.823,400

Welding0.61.01.223,400

Painting1.42.63.146,800

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.

b.Solve the model without the auxiliary variables and explain the relationship between the reduced costs and the shadow prices found in part a.

My question is this, I have put everything into my Excel solver but I am not sure how to come to the answer.

in other words, i know that the best production values are 16157 small, 6200 medium, and 2600 large and that the profit will be $651,221.43 but how does the solver come to this answer? I need to be able to explain my answer but I'm not sure how.