Question

A brokerage firm has just been instructed by one of its clients to invest $600,000 of her money. The analysts at the brokerage firm are considering the following options for investment:

                                             

                                            Projected Rate

Investment Option            of Return (%)

Municipal bonds                          2.4

Company A stocks                      8.0

Company B stocks                      10.2     

Company C stocks                       9.5

The client has specified the following guidelines:

- Municipal bonds should constitute at least 30% of the money invested.

- At least 50% of the funds available should be placed in a combination of A, B, and C stocks.

- No more than 60% of the amount invested in municipal bonds should be invested in stock B.

- All money must be invested.

The client’s goal is to maximize total projected return on investments.

Formulate a linear programming 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

LP model is following:

(a) Decision variables: Let M, A, B, C be the amount to be invested in Municipal bonds, Company A, B and C stocks respectively

(b) Objective: Max 2.4M + 8A + 10.2B + 9.5C

(c) Constraints:

M >= .3(M+A+B+C)  (Municipal bonds should constitute at least 30% of the money invested)

A+B+C >= .5*600000 (at least 50% of funds should be invested in combination of A, B and C stock)

B <= .6M (No more than 60% of amount invested in Municipal bonds should be invested in stock B)

M+A+B+C = 600000 (all money must be invested)

M, A, B, C >= 0 (non-negativity constraint)