HW$8($CH$12)-$ Linear optimization

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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 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 $240.$

$($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 the constant is $"1"$ it must be entered in the box. If your answer is zero enter $"0".$