A recent MBA graduate, Dara, has gained control over custodial accounts that her parents had established. Currently, her money is invested in four funds $($large cap blend, small cap growth, green fund, and growth and income$),$ but she has identified several other funds as options for investment. She has $$100,000$ to invest with the following restrictions:

Keep at least $$5,000$ in a savings account.

Invest at least $14\%$ in the money market fund.

Invest at least $16\%$ in international funds $($small cap international and$/$or emerging international$).$

Keep at least $35\%$ of funds in current holdings.

Do not allocate more than $20\%$ of funds to any one investment except for the money market and savings account.

Allocate at least $30\%$ into new investments.

$\backslash$table$[[,$Average Return,Expenses,$],[1.$ Large cap blend,$17\mathrm{.}2\%,0\mathrm{.}93\%,($current holding$)],[2.$ Small cap growth,$20\mathrm{.}4\%,0\mathrm{.}56\%,($current holding$)],[3.$ Green fund,$26\mathrm{.}3\%,0\mathrm{.}70\%,($current holding$)],[4.$ Growth and income,$15\mathrm{.}6\%,0\mathrm{.}92\%,($current holding$)],[5.$ Multicap growth,$19\mathrm{.}8\%,0\mathrm{.}92\%,],[6.$ Midcap index,$22\mathrm{.}1\%,0\mathrm{.}22\%,],[7.$ Multicap core,$27\mathrm{.}9\%,0\mathrm{.}98\%,],[8.$ Small cap international,$35\mathrm{.}0\%,0\mathrm{.}54\%,],[9.$ Emerging international,$36\mathrm{.}1\%,1\mathrm{.}17\%,],[10.$ Money market fund,$4\mathrm{.}75\%,0,],[11.$ Savings account,$1\mathrm{.}0\%,0,]]$

Develop a linear optimization model to maximize the net return. Interpret the sensitivity report.

Hints:

The net return for an investment is simply the difference between the average return and the expenses.

The decision variables are the amount $($$$)$ to allocate to each investment.