Blair & Rosen, Inc. (B&R), is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of it clients. A client who contacted B&R this past week has a maximum of $50,000 to invest. B&R’s investment advisor has decided 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 $35,000 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 more risky of the two investment alternatives, has a risk rating of 6 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 6(10) + 4(10) = 100. Finally, B&R has 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 have classified the current client as a moderate investor. B&R recommends that a client who is moderate investor limit his or her portfolio to a maximum risk rating of 240. What is the recommended investment portfolio for this client? What is the annual return for the portfolio?
Formulate this program, i.e. define two variables, an objective function, three constraints, and non-negativity constraints. Solve it graphically and specify the optimal solution.