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 $$50,000$ to invest. B&R$$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 $12\%,$ while 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 thousand dollars invested. The Blue Chip fund has a risk rating of $4$ per thousand dollars invested. For example, if $$10,000$ is invested in each of the two investment funds, B&R$$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 $240.$

What is the recommended investment portfolio for this client? What is the annual return for the portfolio? When required, round your answers to the nearest dollar.

Internet fund $fill in the blank $1$

Blue Chip fund $fill in the blank $2$

Annual return $fill in the blank $3$

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 recommended investment portfolio for this aggressive investor? When required, round your answers to the nearest dollar.

Internet fund $fill in the blank $4$

Blue Chip fund $fill in the blank $5$

Annual return $fill in the blank $6$

Discuss what happens to the portfolio under the aggressive investor strategy.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

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 an amount is zero, enter $"0".$ When required, round your answers to the nearest dollar.

Internet fund $fill in the blank $8$

Blue Chip fund $fill in the blank $9$

Annual return $fill in the blank $10$

Discuss the interpretation of the slack variable for the total investment fund constraint.