Klein Industries manufactures three air compressors: small, medium, and large, which have unit profits of $20.50, $34, and $42 respectively. The monthly projected sales of small are a minimum of 14,000 and a maximum of 21,000. Projected sales for medium is projected to be at least 6200 with a maximum of 12500. And large is projected to have a minimum of 2600 and a max of 4200. Production is complete in three steps time is given per minute. Bending and forming; small 0.4+ medium 0.7 + large 0.8 is less than or equal to 23,400 minutes. Welding; small 0.6 + medium 1 + large 1.2 is less than or equal to 23,400 minutes. Painting; small 1.4 + medium 2.6 + large 3.1 is less than or equal to 46,800 minutes. 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.