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 $2.15 million in three investment funds: stock fund A, stock fund B and a money market fund. Stock fund A provides an annual rate of return of 10%, stock fund B provides an annual rate of return of 14% and the money market fund provides an annual rate of return of 4%. The client wants to minimize the total risk index subject to the requirement that the total annual return on the investment be no less than $2.65 million. According to Innis’s risk measurement system, each dollar invested in stock fund A has a risk index of 0.8, each dollar invested in stock fund B has a risk index of 0.7 and each dollar invested in the money market fund has a risk index of 0.2; 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 $300,000 be invested in stock fund A. The amount invested in stock fund B must be at least 18% of the total investment.The amount invested in the money market must be within +/- 12% of the total amount invested in stocks.
Formulate a Linear Programming model to determine optimal investment amounts.