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 $$50,000$ to invest. B&R$\text{'}$s investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of $12\%,$ and the Blue Chip fund has a projected annual return of $9\%.$ The investment advisor requires that at most $$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 the more risky of the two investment alternatives, has a risk rating of $6$ per $$1,000$ invested. The Blue Chip fund has a risk rating of $4$ per $$1,000$ 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 $6(10)+4(10)=100.$ 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 $240.$

$($a$)$ Formulate a linear programming model to find the best investment strategy for this client.

Let $1=$ Internet fund investment in thousands

B $=$ Blue Chip fund investment in thousands

If required, round your answers to two decimal places. If the constant is $"1"$ it must be entered in the box. If your answer is zero, enter $"0".$

Max

$0\mathrm{.}12$

$1+$

$0\mathrm{.}09$

s$.$t$.$

$1$

I$+$

$1$

B $<=$

$$

$

Available investment funds

$1$

I $+$

$<$

$

Maximum investment in the internet fund

$6$

$4$ B$<=$

Maximum risk for a moderate investor

$1,$ B

$($b$)$ Build a spreadsheet model and solve the problem using Excel Solver. What is the recommended investment portfolio for this client?

Internet Fund $=$ $

$20,000$

Blue Chip Fund $=$ $

$30,000$

What is the annual return for the portfolio?

$5,100$

$($c$)$ Suppose that a second client with $$50,000$ to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is $320.$ What is the recy mended investment portfolio for this aggressive investor?

Internet Fund $=$ $

$35,000$

Blue Chip Fund $=$ $

$15,000$

Annual Return $=$ $

$5,550$

$($d$)$ Suppose that a third client with $$50,000$ to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is $160.$ Develop the recommended investment portfolio for the conservative investor. If your answer is zero, enter $"$O$"$

Internet Fund $=$ $

Blue Chip Fund $=$ $

$40,000$

Annual Return $=$ $

$3,600$