# solution

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 dierent investment objectives and dierent tolerances for risk. To
accommodate these dierences, Pfeier 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 6% 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, nd the optimal solution, objective
function and sensitivity report.
3. How much may the yields on the three funds vary before it will be necessary for Yorktown to modify
Mikayla’s portfolio?
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 0.09, how would you
recommend modifying Mikayla’s portfolio?

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