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
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ad24375-0e35-46d0-ae73-58d7d895a57f%2Ffa77a7c9-ed0c-4a94-b6a7-d05b0daea169%2F59txm79_processed.jpeg&w=3840&q=75)
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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