(5 points) Develop a linear optimization model in Excel to determine the optimal investment strategy that will provide maximum yield subject to all the constraints given in the problem; (Hint: design the spreadsheet such that it will be easy to carry out sensitivity analysis for parameter changes included in the Q3 below; also, be careful in calculating the portfolio yield and risk index, and in specifying the limit on risk index in the Solver) 2. (5 points) Using the parameters mention in the case problem for the yields and the risk indicators for each investment fund for a client who has $800K to invest and has acceptable maximum risk index of 0.05, run the optimization model to recommend investments in each of the three funds; also indicate the annual yield from the recommended portfolio, risk index for that portfolio and comment on what may be limiting the yield 3. (6 points) Carry out sensitivity analysis for each of the three changes mentioned below to determine optimal investments in each of the three funds, the annual yield for that portfolio, risk index for that portfolio and comment on what may be limiting the yield a. If the client is a risk taker who can accept higher risk index of 0.75; b. Referring to the parameters given in the original situation, if the yield on growth fund is higher at 20% and its risk is also higher at 0.15; c. Referring to the parameters given in the original situation, if the client adds a new constraint that the amount invested in growth fund should not exceed the amount invested in the income fund

J. D. Williams, Inc., is an investment advisory firm that manages more than $120 million in funds for its numerous clients. The company uses an asset allocation model that rec- ommends the portion of each client's portfolio to be invested in a growth stock fund, an income fund, and a money market fund. To maintain diversity in each client's portfolio, the firm places limits on the percentage of each portfolio that may be invested in each of the three funds. General guidelines indicate that the amount invested in the growth fund must be between 20% and 40% of the total portfolio value. Similar percentages for the other two funds stipulate that between 20% and 50% of the total portfolio value must be in the income fund, and at least 30% of the total portfolio value must be in the money market fund. In addition, the company attempts to assess the risk tolerance of each client and ad- just the portfolio to meet the needs of the individual investor. For example, Williams just contracted with a new client who has $800,000 to invest. Based on an evaluation of the client's risk tolerance, Williams assigned a maximum risk index of 0.05 for the client. The firm's risk indicators show the risk of the growth fund at 0.10, the income fund at 0.07, and the money market fund at 0.01. An overall portfolio risk index is computed as a weighted average of the risk rating for the three funds where the weights are the fraction of the cli- ent's portfolio invested in each of the funds. Additionally, Williams is currently forecasting annual yields of 18% for the growth fund, 12.5% for the income fund, and 7.5% for the money market fund. Based on the information pro- vided, how should the new client be advised to allocate the $800,000 among the growth, income, and money market funds? Develop a linear programming model that will provide the maximum yield for the portfolio. Use your model to develop a managerial report. J. D. Williams, Inc., is an investment advisory firm that manages more than $120 million in funds for its numerous clients. The company uses an asset allocation model that rec- ommends the portion of each client's portfolio to be invested in a growth stock fund, an income fund, and a money market fund. To maintain diversity in each client's portfolio, the firm places limits on the percentage of each portfolio that may be invested in each of the three funds. General guidelines indicate that the amount invested in the growth fund must be between 20% and 40% of the total portfolio value. Similar percentages for the other two funds stipulate that between 20% and 50% of the total portfolio value must be in the income fund, and at least 30% of the total portfolio value must be in the money market fund. In addition, the company attempts to assess the risk tolerance of each client and ad- just the portfolio to meet the needs of the individual investor. For example, Williams just contracted with a new client who has $800,000 to invest. Based on an evaluation of the client's risk tolerance, Williams assigned a maximum risk index of 0.05 for the client. The firm's risk indicators show the risk of the growth fund at 0.10, the income fund at 0.07, and the money market fund at 0.01. An overall portfolio risk index is computed as a weighted average of the risk rating for the three funds where the weights are the fraction of the cli- ent's portfolio invested in each of the funds. Additionally, Williams is currently forecasting annual yields of 18% for the growth fund, 12.5% for the income fund, and 7.5% for the money market fund. Based on the information pro- vided, how should the new client be advised to allocate the $800,000 among the growth, income, and money market funds? Develop a linear programming model that will provide the maximum yield for the portfolio. Use your model to develop a managerial report