The Yorktown Company manages approximately $15 million for clients. For each client, Yorktown chooses a mix of three inv

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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 at least 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
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