FinalExam-Practice-Solutions

FinalExam-Practice-Solutions - Decision Modeling and...

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Decision Modeling and Applications MBAC6080, Spring 2006 Instructor: Thomas Vossen Final Exam - Practice Score:________ Max: 100 points Name:__________________________________ Instructions: Make sure to sign the honor code pledge ! I cannot accept exams without your signature. For full credit, complete solutions must be provided to all problems. An answer without motivation or explanation is not acceptable. I expect that you clearly organize and format the answers to the solutions . Note: Carefully read the questions before you start working on the solutions. Clearly state your assumptions (if any), and try to keep your solutions as simple as possible. Honor Code Pledge “On my honor, as a University of Colorado at Boulder student, I have neither given nor received unauthorized assistance on this work.” Signature:____________________________
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Question 1: LP Formulation Broker Steve Johnson is currently trying to maximize his profit in the bond market. Four bonds are available for purchase and sale, with the bid and ask price of each bond as shown in the following table. Bond Bid Price Ask Price 1 980 990 2 970 985 3 960 972 4 940 954 Steve can buy up to 1,000 units of each bond at the ask price or sell up to 1,000 units of each bond at the bid price. During each of the next 3 years, the person who sells a bond will pay the owner of the bond the cash payments shown in the following table. Year Bond 1 Bond 2 Bond 3 Bond 4 1 100 80 70 60 2 110 90 80 50 3 1,100 1,120 1,090 1,110 Steve’s goal is to maximize his revenue from selling bonds less his payment for buying bonds, subject to the constraint that after each year’s payments are received, his current cash position is non-negative. Formulate an LP formulation to maximize net profit from buying and selling bonds. SOLUTION: a) Decision Variables (6pts) B1, B2, B3, B4 ≥ 0 “units bought of each bond” S1, S2, S3, S4 ≥ 0 “units bought of each bond” C0, C1, C2, C3 ≥ 0 “cash position at end of each year” b) Objective function (4pts) Max C3
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c) Constraints (6pts) 980S1 + 970S2 + 960S3 + 940S4 – 990B1 - 985B2 – 972B3 – 954B4 = C0 -100S1 - 80S2 - 70S3 - 60S4 + 100B1 + 80B2 + 70B3 + 60B4 + C0 = C1 -110S1 - 90S2 - 80S3 - 50S4 + 110B1 + 90B2 + 80B3 + 50B4 + C1 = C2 -1100S1 -1120S2 -1090S3 -1110S4 + 1100B1 + 1120B2 + 1090B3 + 1110B4 +C2 =C3
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This note was uploaded on 06/01/2008 for the course MBAC 6080 taught by Professor Vossen during the Spring '08 term at Colorado.

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FinalExam-Practice-Solutions - Decision Modeling and...

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