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 $$60,000$ to invest. B&R$\text{'}$s investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of $6\%,$ whereas the Blue Chip fund has a projected annual return of $5\%.$ The investment advisor requires that at most $$40,000$ 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 $290.$ As an initial step to help B&R determine the best investment strategy, develop a mathematical model to maximize the expected annual return.

Question $1$

Develop a spreadsheet model and using Excel Solver, determine a recommended investment portfolio $($in dollars$)$ for the client. How much should be recommended for the client to invest in the internet fund? $($Enter an integer with no commas, no dollar sign, and no decimal places. You should enter a numeric answer with no words.$)$

Question $2$

How much should be recommended for the client to invest in the blue chip fund? $($Enter an integer with no commas, no dollar sign, and no decimal places. You should enter a numeric answer with no words.$)$

Question $3$

Use the recommended investment portfolio that you found in part a and part b$.$ What is the expected annual return for the portfolio? $($Enter your answer as an integer with no commas, no dollar sign, and no decimal places. You should enter a numeric answer with no words.$)$

Question $4$

Suppose that a second client with $$60,000$ to invest has been classified as an aggressive investor. $B$&$R$ recommends that the maximum portfolio risk rating for an aggressive investor is $400,$ and at most $$40,000$ of the client's funds should be invested in the Internet fund. For this aggressive investor, how much should be recommended for the client to invest in the blue chip fund? $($Enter your answer as an integer with no commas, no dollar sign, and no decimal places. You should enter a numeric answer with no words.$)$

Question $5$

Suppose that a third client with $$60,000$ to invest has been classified as a conservative investor. $B$&$R$ recommends that the maximum portfolio risk rating for a conservative investor is $240,$ and at most $$40,000$ of the client's funds should be invested in the Internet fund. For this conservative investor, how much should be recommended for the client to invest in the blue chip fund? $($Enter an integer with no commas, no dollar sign, and no decimal places. You should enter a numeric answer with no words.$)$