BUSI 2013 7th Learning Activity Summer 2022 1. (100 points) The Yorktown Company manages approximately $15 million for clients. For each client, Yorktown chooses a mix of three investment vehicles: a growth stock fund, an income fund, and a money market fund. Each client has different investment objectives and different tolerances for risk. To accommodate these differences, Yorktown places limits on the percentage of each portfolio that may be invested in the three funds and assigns a portfolio risk index to each client. Here's how the system works for Mikayla Doucet, one of Yorktown's clients. Based on an evaluation of Mikayla's risk tolerance, Yorktown has assigned Mikayla's portfolio a risk index of 0.1. Furthermore, to maintain diversity, the fraction of Mikayla's portfolio invested in the growth must be atleast 10%, income funds must be at least 15% and at least 20% must be in the money market fund. The risk ratings for the growth, income, and money market funds are 0.10, 0.05, and 0.01, respectively. A portfolio risk index is computed as a weighted average of the risk ratings for the three funds, where the weights are the fraction of the portfolio invested in each of the funds. Mikayla has given Yorktown $350,000 to manage. Yorktown is currently forecasting a yield of 15% on the growth fund, 10% on the income fund, and 8% on the money market fund. 1. Develop a linear programming model to select the best mix of investments for Mikayla's portfolio. 2. Solve the model you developed in part (1). In other words, find the optimal solution, objective function and sensitivity report. 3. How much may the yields on the three funds may vary such that Mikayla's portfolio remains the same? 4. If Mikayla were more risk tolerant, how much of a yield increase could he expect? For instance, what if his portfolio risk index is increased to 0.11? 5. If Yorktown revised the yield estimate for the growth fund downward to 9%, how would you recommend modifying Mikayla's portfolio?