Investment Manager Max Gaines Has Several Clients Who Wish to Own

Investment manager Max Gaines has several clients who wish to own a mutual fund portfolio that matches, as a whole, the performance of the S&P 500 stock index. His 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 S&P 500 index. Formulate the appropriate nonlinear program. $\text { Annual Returns (Flanning Scenarios) }$
$\begin{array}{c|rrrr}\text { Mutual Fund } & \text { Year } 1 & \text { Year 2 } & \text { Year } 3 & \text { Year 4 }\\\hline\text { International Stock } & 26.73 & 22.37 & 6.46 & -3.19 \\\text { Large-Cap Blend } & 18.61 & 14.88 & 10.52 & 5.25 \\\text { Mid-Cap Blend } & 18.04 & 19.45 & 15.91 & -1.94 \\\text { Small-Cap Blend } & 11.33 & 13.79 & -2.07 & 6.85 \\\text { Intermediate Bond } & 8.05 & 7.29 & 9.18 & 3.92 \\\hline \text { S\&P 500 Index } & 21.00 & 19.00 & 12.00 & 4.00\end{array}$