Question

# Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is...

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:

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?

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?

NO. How the optimal solution will change cannot be determined using the Sensitivity Analysis report. Further analysis is required. The traditional sensitivity analysis is only for changes in single coefficient values.

For example in this case, when coefficient of S is changed, the problem will change to a new problem for which the existing sensitivity analysis report may not be applicable.