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 $$55,000$ to invest. B&R$\text{'}$s investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of $12\%,$ and the Blue Chip fund has a projected annual return of $9\%.$ The investment advisor requires that at most $$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 $5$ 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 $5(10)+5(10)=100.$ 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. If an amount is zero, enter $"0".$ If the constant is $"1"$ it must be entered in the box.

$\backslash$table$[[-$ Select your answer $-vv,I+,B,$F$,,],[$s$.$t$.],[,I+,$B$,-$ Select your answer $-vv,$$$,$Available investment funds$],[,I+,$B$,-$ Select your answer $-vv,$$$,$Maximum investment in the internet fund$],[,I+,B,-$ Select your answer $-vv,,$Maximum risk for a moderate investor$],[,,,-$ Select your answer $-vv,,]]$

$($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 angressive 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 reccomends that the maxiamum portfolio risk rating for a consecutive investor is $150.$ Develop the reccomended investment portfolio for the conservative investor. If an amountis zero, enter $"0".$

Internet fund$=$

Blue chip fund$=$

Annual return$=$