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 LargeMinimum 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 eachproduct 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 maximizeprofit? a. Formulate and solve a linear optimization model using the auxiliary variablecells method and write a short memo to the production manager explaining thesensitivity information. b. Solve the model without the auxiliary variables and explain the relationshipbetween the reduced costs and the shadow prices found in part a.