Blair & Rosen, Inc. $($BAR$),$ is a brokerage firm that spedalizes in investment portfollos designed to ment the spacific risk tolorances of its

dlents. A cllent who contacted B$8$R this past week has a maximum of $$.5,$ aq$,$ to invest. BBR$\text{'}$s investment advisor decides to recommend

a portfollo consisting of two investment funds: an intemet fund and a Blue chip fund. The Internet fund has a projected annual return of

$\%,$ whereas the Blue Chip fund has a projected annual retum of $\%\%.$ The investment advisor requires that at most $$50,000$ of the

dient's funds should be Invested in the Intemet fund, BBR services indude 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 imvested. 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 imvestment funds, B$8$R$\text{'}$s risk

rating for the portfollo would be $6(10)+4(10)=100.$ Finally, B$8$R developed a questlonnaire to measure each cllent's risk tolerance.

Based on the responses, each cllent is classlfied as a conservative, moderate, or aggresslve investor. Suppose that the questionnalre

results classified the current cllent as a moderate Investor. B$8$R recommends that a cllent who is a moderate investor limit his or her

portiolio to a maximum risk rating of aco.

$($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$0\mathrm{.}06N+0\mathrm{.}05B$

s$.$t$.$

Avallable investment funds

$N+B75$

Maximum investment in the internet fund

$N50$

Maximum risk for a moderate investor

$6N+4B360$

$N,B0$

$($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 $s$

blue chip fund $s$

$x$

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

$5$

$x$

$($b$)$ Suppose that a second client with $575,000$ to invest has been classified as an aggressive investor. B$8$R recommends that the

maximum portfolio risk rating for an aggressive investor is $400.$ What is the recommended investment portfolio $($in dollars$)$ for this

aggressive investor?

internet fund $s$

$$

blue chip fund $?$

$x$

Suppose that a third cflent with S$/$S$,000$ to invest has been classiffed as a conservative investor: BSR recommends that the

maximum porffolio risk rating for a conservative investor is $200.$ Develop the recommended investment portfollo $($in dollars$)$ for the

conservative investor.

internet fund, $s$

blue chip fund $