# What is the optimal solution, and what is the minimum total risk?

Innis consulting group 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 fund costs \$50 and provides an annual rate of return of \$5 per dollar invested ; each unit of the money market fund costs \$100 and provides an annual rate of return of \$4 for each dollar invested . 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 specified that at least \$3000 be invested in the money market fund.

a. Determine how many units of each fund Innis should purchase for the client to minimize the total risk index for the portfolio.

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b. How much annual income will this investment strategy generate?

c. Suppose the client desires to maximize annual return. How should the funds be invested?

d. What is the optimal solution, and what is the minimum total risk?

e. Specify the objective coefficient ranges.

f. How much annual income will be earned by the portfolio?

g. What is the rate of return for the portfolio?

h. What is the dual value for the funds available constraint?

i. What is the marginal rate of return on extra funds added to the portfolio?

j. Suppose the risk index for the stock fund (the value of CS) increases from its current value of 8 to 12. How does the optimal solution change, if at all?k. Suppose the risk index for the money market fund (the

value of CM) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all?

l. Suppose CS increases to 12 and CM increases to 3.5. How does the optimal solution change, if at all?

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