Lymann Brothers Has a Substantial Number of Clients Who Wish

Lymann Brothers has a substantial number of clients who wish to own a mutual fund portfolio that closely matches the performance of the S&P 500 stock index.A manager at Lymann Brothers has selected five mutual funds that will be considered for inclusion in the portfolio.The manager must decide what percentage of the portfolio should be invested in each mutual fund. $$\begin{array}{l}\text { Annual Returns (Planning Scenarios) }\\\begin{array} { l r r r r } \text { Mutual Fund } & \text { Year 1 } & \text { Year 2 } & \text { Year3 } & \text { Year 4 } \\\hline \text { International Stock } & 25.64 & 27.62 & 5.80 & - 3.13 \\\text { Large-Cap Blend } & 15.31 & 18.77 & 11.06 & 4.75 \\\text { Mid-Cap Blend } & 18.74 & 18.43 & 6.28 & - 1.04 \\\text { Small-Cap Blend } & 14.19 & 12.37 & - 1.92 & 7.32 \\\text { Intermediate Bond } & 7.88 & 9.45 & 10.56 & 3.31 \\\hline \text { S\&P 500 } & 13.00 & 12.00 & 7.00 & 2.00\end{array}\end{array}$$ Minimize the variance of the portfolio subject to constraints on the expected return,assuming that Lymann Brothers' client requires the expected portfolio return to be at least 9 percent.

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Define the Objective Function
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