$[15]$ West Coast Investing $($WCI$)$ is building a portfolio from three investments: $1,2,$ and $3.$ WCI has

$8$ years of annual return data to work from. This information is in the workbook that accompanies

this exam. The goal for WCI is to determine the optimal portfolio, that is$,$ the optimal allocation

of the client's funds to these three investments.

$($c$)[4]$ Suppose that WCI seeks a portfolio that maximizes its utility function, which is a linear

combination of the portfolio return and the portfolio risk $($standard deviation$).$ To characterize

the trade$-$off between return and risk in the utility function, every $1\%$ decrease in risk is

equivalent to every $1\mathrm{.}5\%$ increase in return. Formulate this portfolio optimization problem as

a nonlinear program. Clearly define your decision variables, objective function, and constraints.

Write the objective and constraints in math formulas. $($Hint: Both the portfolio return and

risk should appear in the objective function$)$

$($d$)[4]($Excel$)$ Set up and solve the nonlinear program in part $($c$)$ in the Excel workbook $($Sheet

WCI$-$d$).$ What is the optimal allocation of funds? What is the overall return and risk of your

portfolio? Write down the answers here and save the Answer report in Excel.