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:

PROJECT NPV YEAR 1 YEAR 2 YEAR 3

Condominium 300 64 60 58

Shopping center 290 50 45 58

Warehouse 250 50 32 60

Business Office Building 240 55 45 38

Sports Arena 275 50 44 40

The company has $2,500,000 to invest in year 1, $1,850,000 to invest in year 2 and $2,300,000 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.

a. Formulate an integer optimization model for this problem to maximize the total NPV in this situation by defining the decision variables, the objective function and all the constraints. What type of integer optimization model is this? Briefly describe what the objective function and each constraint represent.

b. The optimal solution for the above problem is given below.

Variable values are X1 = 1, X2 = 1, X3 = 1, X4 = 0, X5 = 1

Objective function value is 1115

Interpret the optimal solution to make a recommendation to the company.