Let us consider again the investment data from Hauck Financial Services used in Section 10.4 to illustrate the Markowitz portfolio model. The data follows, along with the return of the S&P 500 Index. Hauck would like to create a portfolio using the funds listed, so that the resulting portfolio matches the return of the S&P 500 index as closely as possible.

a. Develop an optimization model that will give the fraction of the portfolio to invest in each of the funds so that the return of the resulting portfolio matches as closely as possible the return of the S&P 500 Index. (Hint: Minimize the sum of the squared deviations between the portfolio€™s return and the S&P 500 Index return for each year in the data set.)
b. Solve the model developed in part a.

Mutual Fund Year 1 Year 2 Year 3 Year 4 Year 5 10.060 13.120 13.470 45.420 21.930 Foreign Stock Intermediate-Term Bond 17.640 3.250 75101.330 Large-Cap Growth Large-Cap Value Small-Cap Growth 7.360 32410 18.710 33.280 41.460-23.260 32.360 20.610 12.930 7.060 -5.370 9.020 Small-Cap Value S&P 500 Return 3.440 19.400 3850 58.680 24.560 5.320 6.700 5.430 17.310 25.000 20.000 8.000 30.000-10.000