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 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.
Solution Tip: You must use Solver tool in Excel. Set your constraints right, and fill in the solver dialogue box properly. Be sure to review links provided in the last lesson, or in one of the announcements in the first week of class. Here is a You Tube link you could view:
Given that many of you had issues downloading and setting up Premium Solver's 15-day trial version, I will give you full credit for the homework assignment if you do the following:
- Correctly set up and solve the Excel optimization problem that will result in the correct production decision and profit maximization. Please remember that you must include your Excel spreadsheet in your submission.
- Draft a managerial memo (either in MS Word or MS Excel) that will discuss:
- Profit optimization decision and the number of units produced.
- Binding constraints of your production process.
- Managerial actions that should be taken in the future to increase maximum profits (these should be based on your binding constraints - e.g., can you increase capacity of your plant to eliminate bottlenecks?)
If you are able to provide sensitivity and shadow price analysis, you will receive extra credit - up to 15 additional points.