SolveÿProblem and Applications: ÿThe data is given as part of the question. There is no external data set provided. Use what is given by the problem.ÿ13-7. ÿKlein Industries manufactures three types of portableÿair compressors: small, medium, and large, which haveÿunit profits of \$20.50, \$34.00, and \$42.00, respectively.ÿThe projected monthly sales are:ÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿSmall ÿMedium ÿLargeÿÿMinimum ÿ14,000 ÿ 6,200 ÿ2,600ÿÿMaximum ÿ21,000 ÿ12,500 ÿ4,200ÿÿÿThe 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:ÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿSmall ÿMedium ÿLarge ÿAvailable Time ÿBending/forming ÿÿÿÿÿÿÿ ÿ ÿ0.4 ÿÿÿÿÿÿ0.7 ÿÿÿÿÿÿ0.8 ÿÿÿÿÿÿ23,400ÿWelding ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ0.6 ÿÿÿÿÿÿ1.0 ÿÿÿÿÿÿ1.2 ÿÿÿÿÿÿ23,400ÿPainting ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿ ÿÿ1.4 ÿÿÿÿÿÿ2.6 ÿÿÿÿÿÿ3.1 ÿÿÿÿÿÿ46,800ÿÿ ÿHow many of each type of air compressor should the company produce to maximize profit?ÿÿa. ÿFormulate 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.ÿÿb. ÿSolve the model without the auxiliary variables and explain the relationship between the reduced costs and the shadow prices found in part a.ÿSolution Tip: You must use Solver tool in Excel. Set your constraints right, and fill in the solver dialogue box properly. Here is a You Tube link you could view:ÿhttp://www.youtube.com/watch?v=Oyc0k9kiD7o