# 9050

**Investment Problem**

1. Innis consulting group Investments manages funds for a number ofcompanies and wealthy clients. The investment strategy is tailored to eachclient’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 andprovides an annual rate of return of $4 for each dollar invested. The clientwants to minimize risk subject to the requirement that the annual income fromthe investment be at least $60,000. According to Innis’s risk measurementsystem, each unit invested in the stock fund has a risk index of 8, and eachunit invested in the money market fund has a risk index of 3; the higher riskindex associated with the stock fund simply indicates that it is the riskier investment.Innis’s client also specified that at least $300,000 be invested in the moneymarket fund.

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

b. How much annual income willthis investment strategy generate?

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

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

e. Specify the objectivecoefficient ranges.

f. How much annual income willbe earned by the portfolio?

g. What is the rate of returnfor the portfolio?

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

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

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

k. Suppose the risk index forthe money market fund (the value of CM) increases from its current value of 3to 3.5. How does the optimal solution change, if at all?

l. Suppose CS increases to 12 and CM increases to3.5. How does the optimal solution change, if at all?