4. A real estate company is considering five possible projects: a small condominium complex, a small shopping center, a warehouse, a small business office building and a sports arena. Each of these projects requires different funding over the next three years, and the net present values of the projects also varies. The following table provides the required investment amounts (in $10,000s) and the net present value, NPV (in $10,000s), of each project:

PROJECTNPV YEAR 1YEAR 2 YEAR 3

Condominium 250 64 60 58

Shopping center 240 50 4558

Warehouse20050 3260

Business Office Building190554538

Sports Arena 225 50 4440

The company has $2,600,000 to invest in year 1, $1,950,000 to invest in year 2 and $2,400,000 in year 3. The company wants to select at least 3 projects. In addition, the company also wants to select at least one project from the shopping center and sports arena projects.

Develop a capital budgeting formulation to maximize the total NPV in this situation by

(a) Defining the decision variables.

(b) Determining the objective function. What does it represent?

(c) Determining all the constraints. What does each constraint represent?

Note: Do NOT solve the problem after formulating.