Math 464 Final Exam

# Math 464 Final Exam - Math 464Operations Research and Game...

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Math 464–Operations Research and Game Theory Spring 2006 Final Take-Home Examination 1. Your responses to the questions in this examination are due no later than 10:00 a.m. on Monday, May 1, 2006, in mail box marked ‘Ariyawansa’ in Neill 103. No late submission or solutions submitted elsewhere will be accepted. 2. Please note that there are 7 questions in the following 3 pages. Respond to all the questions. The maximum number of points given for each part of each question is indicated within brackets in the left margin. 3. Complete and sign the statement below and return this page with your solutions . No credit will be given for solutions submitted without this page duly signed. I certify that the solutions provided by me for problems in the final take-home examination of the course Operations and Research and Game Theory, Math 464, Spring 2006, are based only on my personal efforts. Name: Signature: Date: 1

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[14] 1. A manufacturing company which produces a single type of item wishes to enlarge its capacity over the next six production periods (a period is three months). The com- pany’s objective is to have its production capacity as large as possible by the beginning of the seventh period. Each item produced in a period requires \$ 100 (for the purchase of raw materials and the payment of wages of employees) at the beginning of that period, and one unit of plant capacity; it yields \$ 140 of sales revenue at the beginning of the next period . In each period, the company can use either or both of two construction techniques to expand its plant. These two techniques are termed Expansion Method I and Expan- sion Method II. Both expansion methods can only be initiated at the beginning of a period, and each requires cash when the expansion is initiated. Expansion Method I
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