A second version of the Markowitz portfolio model maximizes expected return subject to a constraint that the variance of the portfolio must be less than or equal to some specified amount. Consider the Hauck Financial Service data. We list the data again below 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. Click on the datafile logo to reference the data. DATA Mutual Fund Foreign Stock Intermediate-Term Bond 17.64 3.25 7.51 1.33 7.36 Large-Cap Growth Large-Cap Value Small-Cap Growth Small-Cap Value S&P 500 Return Year 1 Year 2 Year 3 Year 4 Year 5 10.06 13.12 13.47 45.42 21.93 32.41 18.71 33.28 41.46 -23.26 32.36 20.61 12.93 7.06 5.37 33.4419.4 3.8558.689.02 24.56 25.32 6.7 5.43 17.31 -10 25 20 30 (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. Let FS- proportion of portfolio invested in the foreign stock mutual fund IB = proportion of portfolio invested in the intermediate-term bond fund LG = proportion of portfolio invested in the large-cap growth fund LV proportion of portfolio invested in the large-cap value fund SG = proportion of portfolio invested in the small-cap growth fund SV-proportion of portfolio invested in the small-cap value fund Ds the difference between the portfolio return and the S&P 500 return, years