Management Science 345 Linear Programming Challenge- Financial Portfolio Optimization Chapter 7vO You work for an investment advisory firm that manages more than $250 million in funds for various clients. The company uses an asset allocation model that client's portfolio be invested in a growth stock fund, an income fund, and a money market fund Risk for each client is managed through diversification of each client's portfolio. The firm places recommends a portion of each imits 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 adjust the portfolio to meet the needs of the individual investor. You have been given your first client, who has $800,000 to invest toward retirement. Your client wants her portfolio maximized for the highest possible return based on the firm's diversification principles stated previously. After conducting an evaluation of your client's risk tolerance, you have assigned a maximum risk index of 0.05. The firm's 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 o the client's portfolio invested in each of the fynds Additionally, the firm 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 provided, how should your client be advised to allocate the $800,000 among the three funds. Develop a ear programming model that will provide the maximum yield for the portfolio. Included in your report should be answers to the following: 1. Recommend how much of the $800,000 should be invested in each of the three funds. What is the annual yield you anticipate for the investment recommendation? 2. If you could convince your client to increase their risk index to 0.055, how much would the yield increase and how would the investment recommendation change? 3. If the annual yield for the growth fund were revised downward to 16%, how would the overall yield change along with the recommendation for the three funds? Assume original risk tolerance of 0.05 4. Assume the client expressed some concern about having too much money in the growth fund. How would the original recommendation change if the amount invested in the growth fund is not allowed to exceed the amount invested in the income fund