Signs < = > Data Objective Min. Demand for Small MAX. Demand for Small Min. Demand for Med MAX. Demand for Med Min. Demand for Large MAX. Demand for Large Bending/Forming Welding Painting Results Variables Objective Small Medium Large $ 20.50 $ 34.00 $ 42.00 1 1 1 1 1 1 0.4 0.7 0.8 0.6 1 1.2 1.4 2.6 3.1 Sign > < > < > < < < < RHS 14000 21000 6200 12500 2600 4200 23400 23400 46800 Results LHS Slack/Surplus Excel work in SOLVER is required for this assignment as an original sheet with the all details of work and calculations included. 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 air compressors: small, medium, and large, which have unit profits of $20.50, $34.00, and $42.00, respectively. The projected monthly sales are: 13-7. Klein Industries manufactures three types of portable 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 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. LP Solver.xlsx