XYZ Mutual Fund is seeking to invest $80 million in real estate projects with high potential returns. The fund has identified several investment opportunities, each with a specific investment cost and expected economic benefit (see the table below). The goal is to maximize the total economic benefit by selecting a combination of projects to invest in while staying within the budget mentioned above. However, there are several constraints to consider, including the requirement to invest in at least four projects in total, with at least two of them being environmentally friendly (projects that are considered environmentally friendly are: 3, 5, 9, and 10). Additionally, if project 3 is selected, then project 4 must also be chosen, but project 4 can be chosen independently of project 3. The fund cannot make partial or fragmented investments, and projects cannot be purchased multiple times as each project is unique. The challenge is to determine the optimal combination of projects that will maximize the total economic benefit while adhering to these constraints. Investment cost ($ millions) Expected economic benefit ($ millions) Project 1 21 49 Project 2 18 48 Project 3 20 33 Project 4 25 45 Project 5 13 36 Project 6 10 47 Project 7 22 50 Project 8 24 35 Project 9 21 43 Project 10 24 30 1. Formulate an optimization model below (decision variables, objective function, and constraints) to help the company decide which projects to invest the money in. 2. Write and explain the problem's optimal numerical solution (optimal value for the objective function and decision variables)
XYZ Mutual Fund is seeking to invest $80 million in real estate projects with high potential returns. The fund has identified several investment opportunities, each with a specific investment cost and expected economic benefit (see the table below). The goal is to maximize the total economic benefit by selecting a combination of projects to invest in while staying within the budget mentioned above. However, there are several constraints to consider, including the requirement to invest in at least four projects in total, with at least two of them being environmentally friendly (projects that are considered environmentally friendly are: 3, 5, 9, and 10). Additionally, if project 3 is selected, then project 4 must also be chosen, but project 4 can be chosen independently of project 3. The fund cannot make partial or fragmented investments, and projects cannot be purchased multiple times as each project is unique. The challenge is to determine the optimal combination of projects that will maximize the total economic benefit while adhering to these constraints.
|
|
Investment cost ($ millions) |
Expected economic benefit ($ millions) |
|
Project 1 |
21 |
49 |
|
Project 2 |
18 |
48 |
|
Project 3 |
20 |
33 |
|
Project 4 |
25 |
45 |
|
Project 5 |
13 |
36 |
|
Project 6 |
10 |
47 |
|
Project 7 |
22 |
50 |
|
Project 8 |
24 |
35 |
|
Project 9 |
21 |
43 |
|
Project 10 |
24 |
30 |
1. Formulate an optimization model below (decision variables, objective function, and constraints) to help the company decide which projects to invest the money in.
2. Write and explain the problem's optimal numerical solution (optimal value for the objective function and decision variables)
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