Financial Planner Minnie Margin Has a Substantial Number of Clients $\text { Annual Returns (Flanning Scenarios) }$

Essay

Financial planner Minnie Margin has a substantial number of clients who wish to own a mutual fund portfolio that matches, as a whole, the performance of the Russell 2000 index. Her task is to determine what proportion of the portfolio should be invested in each of the five mutual funds listed below so that the portfolio most closely mimics the performance of the Russell 2000 index. Formulate the appropriate nonlinear program. $\text { Annual Returns (Flanning Scenarios) }$
$\begin{array}{c|rrrr}\text { Mutual Fund } & \text { Year } 1 & \text { Year 2 } & \text { Year } 3 & \text { Year 4 }\\\hline \text { International Stock } & 22.37 & 26.73 & 4.86 & 2.17 \\\text { Large-Cap Value } & 15.48 & 19.64 & 11.50 & -5.25 \\\text { Mid-Cap Value } & 17.42 & 20.07 & -4.97 & -1.69 \\\text { Small-Cap Growth } & 23.18 & 12.36 & 3.25 & 3.81 \\\text { Short-Term Bond } & 9.26 & 8.81 & 6.15 & 4.04 \\\hline \text { Russell 2000 Index } & 20.00 & 22.00 & 8.00 & -2.00\end{array}$