The table below shows data on the returns over five 1-year periods for six mutual funds. Returns over Five 1-Year Periods for Six Mutual Funds Planning Scenarios for Next 12 Months Mutual Funds Year 1 Year 2 Year 3 Year 4 Year 5 Large-Cap Stock 35.3 20.0 28.3 10.4 9.3 Mid-Cap Stock 32.3 23.2 0.9 49.3 22.8 Small-Cap Stock 20.8 22.5 6.0 33.3 6.1 Energy/Resources Sector 25.3 33.9 20.5 20.9 2.5 Health Sector 49.1 5.5 29.7 77.7 24.9 Technology Sector 46.2 21.7 45.7 93.1 20.1 Real Estate Sector 20.5 44.0 21.1 2.6 5.1 A firm's portfolio managers will assume that one of these scenarios will accurately reflect the investing climate over the next 12 months. The probabilities of each of the scenarios occurring are 0.1, 0.3, 0.1, 0.1, and 0.4 for years 1 to 5, respectively. (a) Develop a portfolio model for investors who are willing to risk a portfolio with a return no lower than 2%. (Let LS = the proportion of the portfolio invested in a large-cap stock mutual fund, MS = the proportion of the portfolio invested in a mid-cap stock fund, SS = the proportion of the portfolio invested in a small-cap stock fund, ES = the proportion of the portfolio invested in an energy section fund, HS = the proportion of the portfolio invested in a health sector fund, TS = the proportion of the portfolio invested in a technology sector fund, and RS = the proportion of the portfolio invested in a real estate sector fund.) Max s.t. sum of proportions Year 1 returns Year 2 returns Year 3 returns Year 4 returns Year 5 returns LS, MS, SS, ES, HS, TS, RS 0 (b) Solve the model in part (a) and recommend a portfolio allocation for the investor with this risk tolerance. What is the projected return on investment (as a percent)? (Round your answers to three decimal places.) at (LS, MS, SS, ES, HS, TS, RS) = . (c) Suppose an investor wants to develop a portfolio with a risk tolerance of 0%. Modify the constraints of the portfolio model in part (a) to create a portfolio for this investor. Year 1 returns Year 2 returns Year 3 returns Year 4 returns Year 5 returns LS, MS, SS, ES, HS, TS, RS 0 Solve this linear program to create a portfolio for the investor with a risk tolerance of 0%. at (LS, MS, SS, ES, HS, TS, RS) = . (d) Is the expected return higher for investors following the portfolio recommendations in part (c) as compared to the returns for the portfolio in part (b)? The portfolio from part ??? is higher.