How many regular models, supermodels, and deluxe models should the company manufacture in order to maximize profit?

(a) Formulate a linear optimization model for this problem.

(b) Solve this model by using the Excel Solver. Include Excel output with your answer.

(c) Determine the optimal solution. Interpret and make recommendations based on the optimal solution.

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 vary. 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 250 64 60 58

Shopping center 240 50 45 58

Warehouse 200 50 32 60

Business Office Building 190 55 45 38

Sports Arena 225 50 44 40

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.