MBA505 Take-Home Mid-Term Chapters 1-4
Saint Francis University – Spring 2015 – John S. Miko
Due February 24, 2015
(40 points – 10 points each)
Please solve each problem fully and answer any follow-up questions. Circle all answers. For the Linear Program models done in Excel Solver, I would not only like you to print the spreadsheet with the end results but I also want to see the Decision Variables, Objective Function, and Constraints that you modeled using Excel Solver. This portion can be hand written. This is the only way that I can give partial credit for incorrect answers.
1. Creative Sports Designs (CSD) manufactures a standard-size racket and an oversize racket. The firm’s rackets are extremely light due to the use of a magnesium-graphite alloy that was invented by the firm’s founder. Each standard-size racket uses 0.15 kg of the alloy and each oversize racket uses 0.25 kg. Over the next two-week production period, only 100 kg of the alloy are available. Each standard size racket uses 4 minutes of manufacturing time and each oversize racket uses 5 minutes. The profit contributions are $7 for each standard-size racket and $9 for each oversize racket. 80 hours of manufacturing time are available each week. As well, the marketing department has indicated that we should produce at least 100 standard rackets and 100 oversize rackets so that there is product differentiation in the consumer market. How many rackets of each type should CSD manufacture over the next two weeks to maximize the total profit? Assume that because of the unique nature of their products, CSD can sell as many rackets as they produce. a. What is the optimal profit?
b. What constraints are binding?
c. Interpret at least one shadow price?
d. What is the range of optimality for both standard and oversize rackets?
2. Do 3.36 parts a and b only on Page 180 of our textbook
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