J. D. Williams, Inc. is an investment advisory firm that manages more than $120 millionin funds for its numerous clients. The company uses an asset allocation model that recommends the portion of each client's portfolio to be invested in a growth stock fund, anincome fund, and a money market fund. To maintain diversity in each client's portfolio, thefirm places limits on the percentage of each portfolio that may be invested in each of thethree funds. General guidelines indicate that the amount invested in the growth fund mustbe between 20% and 40% of the total portfolio value. Similar percentages for the other twofunds stipulate that between 20% and 50% of the total portfolio value must be in the incomefund and that 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 adjustthe 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'srisk tolerance, Williams assigned a maximum risk index of 0.05 for the client. The firm'srisk indicators show the risk of the growth fund at 0.10, the income fund at 0.07, and themoney 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 client'sportfolio invested in each of the funds.Additionally, Williams is currently forecasting annual yields of 18% for the growthfund, 12.5% for the income fund, and 7.5% for the money market fund. Based on the information provided, how should the new client be advised to allocate the $800,000 amongthe growth, income, and money market funds? Develop a linear programming model thatwill provide the maximum yield for the portfolio. Use your model to develop a managerialreport.

Recommend how much of the $800,000 should be invested in each of the threefunds. What is the annual yield you anticipate for the investment recommendation?

Assume that the client's risk index could be increased to 0.055. How much wouldthe yield increase, and how would the investment recommendation change?3. Refer again to the original situation, in which the client's risk index was assessedto be 0.05. How would your investment recommendation change if the annual yieldfor the growth fund were revised downward to 16% or even to 14%?

QUESTION TO ANSWER:

In the Investment Strategy Case, suppose the maximum acceptable risk for the portfolio is 0.04.Write down the new constraint to limit the portfolio risk to 0.04 using variables G, I, M where

G= amount invested in growth stock fund

I= amount invested in income stock fund

M= amount invested in money market fund