Assignment for Dec 2, 2009

# Assignment for Dec 2, 2009 - ATENEO DE MANILA UNIVERSITY...

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ATENEO DE MANILA UNIVERSITY Graduate School of Business MBA MIDDLE MANAGER PROGRAM MANAGEMENT SCIENCE Integer/Binary Programming Submitted by: Cenon Oriel David Viray Rodolfo Milan Jr. 02 December 2009

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1. In a project selection model involving seven projects (P 1 , P 2 , P 3 , P 4 , P 5 , P 6 7 ), write constraints to satisfy each of the following conditions: 1. Exactly one project from the set (P 1 , P 4 , P 5 ) has to be selected; 2. At most four projects can be invested in ; 3. If investment in P 3 is made, P 6 must also be selected; 4. Projects P 2 and P 5 must both be selected or both be rejected; 5. If investment is made both in P 1 and P 2 , then project P 7 must also be chosen; 6. If project P 6 is selected, then project P 7 cannot be selected 1. P1 + P4 + P5 = 1 2. P1 + P2 + P3 + P4 + P5 + P6 + P7 = 4 3. P3 < P6 4. P2 = P5 5. P1 + P2 < P7 + 1 6. P6 = P7 < 1 2. A research administrator in the Federal Science Foundation is trying to decide which projects to fund for the coming year. She has received the eight proposals listed below. After careful study, she has made a subjective estimate of the value of each project on a scale of 0 to 100. The research administrator wants to find a mix of projects having the greatest total value. However, there are several limitations. First, she has a budget of \$320,000. Second, she must either accept or turn down a project (i.e. no partial funding). Third, certain projects are related. She does not wish to fund both projects G & H; further, project D shout not be funded unless A is also funded (but A can be funded without D) PROJECT COST (\$000s) VALUE A 80 40 B 15 10 C 120 80 D 65 50 E 20 20 F 10 5 G 60 80 H 100 100 Let A be a binary such that A=1 if project A is selected; A= 0 if project is not selected B be a binary such that B=1 if project B is selected; B= 0 if project is not selected C be a binary such that C=1 if project C is selected; C=0 if project is not selected
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Assignment for Dec 2, 2009 - ATENEO DE MANILA UNIVERSITY...

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