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A project manager is considering a portfolio of 5 project investments. The estimated profit for investment opportunity j = 1, 2, ..., 5 is $10, $8, $12, $7, and $9, respectively. Moreover, the estimated capital required for the projects is $15, $10, $18, $12, and $14, respectively.

A project manager is considering a portfolio of 5 project investments. The estimated profit for investment opportunity j = 1, 2, ..., 5 is $10, $8, $12, $7, and $9, respectively. Moreover, the estimated capital required for the projects is $15, $10, $18, $12, and $14, respectively.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 3.6C
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Formulate the problem attached . Do not solve
Portfolio Selection Problem A project manager is considering a portfolio of 5 project investments. The estimated profit for investment opportunity j = 1, 2, ... , 5 is $10, $8, $12, $7, and $9, respectively. Moreover, the estimated capital required for the projects is $15, $10, $18, $12, and $14, respectively. The total amount of capital available for these investments is $50. - Investment opportunities 3 and 4 are mutually exclusive (if project 3 is funded, then project 4 must not be funded). Project 5 cannot be undertaken unless either 3 or 4 is undertaken. At least two and at most four investment opportunities have to be undertaken. If project 2 is funded, then project 5 must be funded. If project 3 is funded, then projects 1 and 2 must not be funded. Formulate this problem using an integer programming model.
Transcribed Image Text:Portfolio Selection Problem A project manager is considering a portfolio of 5 project investments. The estimated profit for investment opportunity j = 1, 2, ... , 5 is $10, $8, $12, $7, and $9, respectively. Moreover, the estimated capital required for the projects is $15, $10, $18, $12, and $14, respectively. The total amount of capital available for these investments is $50. - Investment opportunities 3 and 4 are mutually exclusive (if project 3 is funded, then project 4 must not be funded). Project 5 cannot be undertaken unless either 3 or 4 is undertaken. At least two and at most four investment opportunities have to be undertaken. If project 2 is funded, then project 5 must be funded. If project 3 is funded, then projects 1 and 2 must not be funded. Formulate this problem using an integer programming model.
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