Question

Problem 11-3 Blair & Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $55,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 12%, while the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $25,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 5 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be 5(10) + 5(10) = 100. Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 250.
(a) Formulate a linear programming model to find the best investment strategy for this client. Let I = Internet fund investment in thousands B = Blue Chip fund investment in thousands If required, round your answers to two decimal places. I + B s.t. I + B Available investment funds I + B Maximum investment in the internet fund I + B Maximum risk for a moderate investor I, B 0

(b) Build a spreadsheet model and solve the problem using Solver. What is the recommended investment portfolio for this client? Internet Fund = $ Blue Chip Fund = $ What is the annual return for the portfolio? $

(c) Suppose that a second client with $55,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 310. What is the recommended investment portfolio for this aggressive investor? Internet Fund = $ Blue Chip Fund = $ Annual Return = $

(d) Suppose that a third client with $55,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 150. Develop the recommended investment portfolio for the conservative investor. Internet Fund = $ Blue Chip Fund = $ Annual Return = $

Answer 1

Answer:

a) Formulate a linear programming model to find the best investment strategy for this client as shown below:

Decision variable:

Let,

I = Internet fund investment in thousands

B = Blue Chip fund investment in thousands

Objective Function:

Max Z = 0.12I + 0.09B

Subject to the following constraints:

Investment amountt: I + B $\leq$ 25,000

Risk Rating: $\frac{5}{1000} I$ + $\frac{4}{1000} B$ ≤ 250 or 0.005I + 0.004B ≤ 250

Non-negativity constraint: I, B  ≥ 0

Explanation:

See attached images for b, c and d