Instructions

Blair & Rosen, Inc. $($B&R$),$ is a brokerage firm that specializes in investment portfolios de$-$signed to meet the specific risk tolerances of its clients. A client who contacted $B$&$R$ this past week has a maximum of $$60,000$ to invest. B&R$\text{'}$s investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of $12\%$ whereas the Blue Chip fund has a projected annual return of $10\%.$ The investment advisor requires that at most $$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 $8$ 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, $B$&$R\text{'}$s risk rating for the portfolio would be $8(10)+4(10)=120.$ 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 $550.$

a$.$ What is the recommended investment portfolio for this client? What is the annual return for the portfolio?

b$.$ Suppose that a second client with $$110,000$ to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is $750.$ What is the recommended investment portfolio for this aggressive investor? Discuss what happens to the portfolio under the aggressive investor strategy.

c$.$ Suppose that a third client with $$100,000$ to invest has been classified as a conservative investor. $B$&$R$ recommends that the maximum portfolio risk rating for a conservative investor is $350.$ Develop the recommended investment portfolio for the conservative investor. Discuss the interpretation of the slack variable for the total investment fund constraint.

Please use a graphical solution method and upload your Word file $($or a photocopy of your handwriting$).$