7. Klein Industries manufactures three types of portable air compressors: small,

Question

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 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.

Explanation / Answer

Klein Industries Small Medium Large Total Profit Unit profit $20.50 $34.00 $42.00 $651,221.43 Monthly Sales Small Medium Large Minimum 14,000 6,200 2,600 Maximum 21,000 12,500 4,200 Checking points Minutes Small Medium Large Available Time Time Used Available-Used Bending/Forming 0.40 0.70 0.80 23,400 12882.85714 10,517 Welding 0.60 1.00 1.20 23,400 19014.28571 4,386 Painting 1.40 2.60 3.10 46,800 46800 0 Total production time 2.40 4.30 5.10 Production 16157.14 6200.00 2600.00 Checking points Min 2157.14 0.00 0.00 Max 4842.86 6300.00 1600.00 Total Profit ($) Total Profit ($) = 20.50 small + 34.00 medium + 42.00 large Production constraints: 14,000

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