Question: 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 fund costs $50 and provides an annual rate of return of 10%? each unit of the money market fund 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 has also specified that at least $300,000 be invested in the money market fund.

Letting S = units purchased in the stock fund

M = units purchased in the money market fund

leads to the following formulation:

Min z = 8S+3M

Subject to:

50S + 100M ≤ 1,200,000 (Funds available)

5S + 4M ≥ 60,000 (Annual income)

M ≥ 3,000 (Units in money market)

S, M ≥ 0

Solve the problem using Excel Solver.

a) What is the optimal solution, and what is the minimum risk?

b) What does s₃ = 7,000 represent, a slack or a surplus? Explain what it means for this problem.

c) Specify the objective coefficient ranges.

d) How much annual income will be earned by the portfolio?

e) What is the rate of return for the portfolio?

f) What is the shadow price for the funds available constraint? Explain what it means for this problem.

g) What is the marginal rate of return on extra funds added to the portfolio?

h) Suppose the risk index for the money market fund increases from its current value of 3 to 3.5. How does the optimal solution, if at all? What is the new total risk?