Exercise $18-30$ Algo $($Using Excel$)$

Jim Markowitz is enrolled in a prestigious MBA program and participates in a student investment

fund competition. A total investment amount of $$1,200,000$ is allocated to his portfolio, and he has

three investment options to choose from. The expected returns from the three investment options

are $2\mathrm{.}6\%,3\mathrm{.}7\%,$ and $5\mathrm{.}8\%,$ respectively. One of the competition criteria is to ensure that each

portfolio has a minimum return of $3\mathrm{.}5\%,$ but to increase his chance of advancing to the second

round, Jim needs to minimize the investment risk of his portfolio. He uses the following formula to

estimate his portfolio's

risk: $0\mathrm{.}1521+0\mathrm{.}2322+0\mathrm{.}4123+0\mathrm{.}020712+0\mathrm{.}012313+0\mathrm{.}0943230\mathrm{.}1512+0\mathrm{.}23{22}_{+}{0\mathrm{.}4}_{?}$

$132+0\mathrm{.}020712+0\mathrm{.}012313+0\mathrm{.}094323,$ where $x_1,x_2,$ and $x_3$ are the proportion of his budget

of $$1,200,000($in $\%).$ Help Jim formulate this problem as an NLP model and answer the following

questions. Use $\frac{1}{3}$ of the total investment amount as an initial value for $x_1,x_2,$ and $x_3.$

a$.$ How much money should Jim invest in each of the three investment options? What are the

minimum risk and expected return from the portfolio?

Note: Round "Minimum risk" to $4$ decimal places and other answers to $2$ decimal places.

b$.$ If the required minimum return on investment changes from $3\mathrm{.}5\%$ to $4\mathrm{.}0\%,$ how much

money should Jim invest in each investment option?

Note: Round "Minimum risk" to $4$ decimal places and other answers to $2$ decimal places.