Suppose the risk index for the stock fund (the objective function coefficient for S) increases from its current value of 8 to 12. How does the optimal solution change, if at all? Suppose the risk index for the money market fund (the objective function coefficient for M) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all?
Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client’s needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock funds costs $50 and provides an annual rate of return of 10%; each unit of the money market funds costs $100 and provides an annual rate of return of 4%.
The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis’s risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis’s client also specifies that at least $300,000 be invested in the money market fund.
Assuming that the company wants to minimize the total risk index for the portfolio (Let S=number of units purchased in the stock funds, M=number of units purchased in the money market fund), answer the following questions:
- What is the linear programming model for this problem?
- Find the optimal solution (the minimum total risk) and the sensitivity report using Excel’s solver.
- How much annual income will this investment strategy will generate?
- Suppose the client desires to maximize annual return. How should the funds be invested?
- Specify the objective coefficient
ranges. - What is the rate of return for the portfolio?
- What is the shadow price for the funds available constraint?
- Suppose the risk index for the stock fund (the objective
function coefficient for S) increases from its current value of 8 to 12. How does the optimal solution change, if at all? - Suppose the risk index for the money market fund (the objective function coefficient for M) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all?
- Suppose the objective function coefficient for S increases to 12 and the objective function coefficient for M increases to 3.5. Can you determine how the optimal solution will change using the Sensitivity Analysis report?
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