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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 four investment funds: stock fund A, stock fund B, Bond fund A and a money market fund. Stock fund A provides an annual rate of return of 15%, stock fund B provides an annual rate of return of 12.5%, the bond fund provides an annual rate of return of 8% 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, each dollar invested in Bond fund A has a risk index of 0.4 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 B. The amount invested in stock fund A must be at least 12% of the total investment. The amount invested in the money market must be within +/- 7% of the total amount invested in stocks. Formulate a Linear Programming model to determine optimal investment amounts.
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