Question

5. A brokerage firm has just been instructed by one of its clients to invest $1,000,000 of her money. The client’s goal is to maximize total projected return on investments. The analysts at the brokerage firm are considering the following options for investment:

                                             

                                            Projected Rate

Investment Option            of Return (%)       Risk (%)

Municipal bonds                          2.2                      0.1

Company A stocks                     12.1                      2.5

Company B stocks                       9.4                     1.7

Company C stocks                       7.2                      0.8

The client has specified the following guidelines:

- The total risk should be less than or equal to $12,000.

- Municipal bonds should constitute at least 20% of the money invested.

- At least 60% of the funds available should be placed in a combination of company A, B, and C stocks.

- No more than 35% of the amount invested in municipal bonds should be invested in stock C.

Formulate a linear optimization model for this investment problem.

(a) Define the decision variables.

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

(c) Determine all the constraints. Briefly describe what each constraint represents.

                                              

Note: Do NOT solve the problem after formulating.

Answer 1