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 $$65,000$ to invest. B&R$\text{'}$s investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of $11\%,$ whereas the Blue Chip fund has a projected annual return of $8\%.$ The investment advisor requires that at most $$45,000$ 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 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

$6(10)+4(10)=100.$

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 $310.$

$($a$)$

Formulate a linear programming model to find the best investment strategy for this client. $($Assume N is the amount invested in the internet fund project and B is the amount invested in the Blue Chip fund. Express the amounts invested in thousands of dollars.$)$

Max

s$.$t$.$

Available investment funds

Maximum investment in the internet fund

Maximum risk for a moderate investor

N$,$ B $>=0$

$($b$)$

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

internet fund $

blue chip fund $

What is the annual return $($in dollars$)$ for the portfolio?

$

$($b$)$

Suppose that a second client with $$65,000$ to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is $350.$ What is the recommended investment portfolio $($in dollars$)$ for this aggressive investor?

internet fund $

blue chip fund $

$($d$)$

Suppose that a third client with $$65,000$ to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is $240.$ Develop the recommended investment portfolio $($in dollars$)$ for the conservative investor.

internet fund $

blue chip fund $