2. Vanguard 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, Vanguard has been authorized to invest up to $3 million in five investment funds: stock fund A, stock fund B, Bond fund A, Bond fund B 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%, Bond fund A provides an annual rate of return of 8%, Bond fund B provides an annual return of 9% and the money market fund provides an annual rate of return of 4%. The client wants to maximize return subject to the requirement that the total annual risk index be no more than $2.65 million. According to Vanguard'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, each dollar invested in Bond fund B has a risk index of 0.48 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. Vanguard'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 bond funds must be within +/- 7% of the total amount invested in stocks. Formulate a Linear Programming model to determine optimal investment amounts.

2. Vanguard 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, Vanguard has been authorized to invest up to $3 million in five investment funds: stock fund A, stock fund B,B ond fund A,B ond fund B 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%, Bond fund A provides an annual rate of return of 8%, Bond fund B provides an annual return of 9% and the money market fund provides an annual rate of return of 4%. The client wants to maximize return subject to the requirement that the total annual risk index be no more than $2.65 million. According to Vanguard'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 , each dollar invested in Bond fund B has a risk index of 0.48 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. Vanguard'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 bond funds must be within +/7% of the total amount invested in stocks. Formulate a Linear Programming model to determine optimal investment amounts. 2. Vanguard 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, Vanguard has been authorized to invest up to $3 million in five investment funds: stock fund A, stock fund B,B ond fund A,B ond fund B 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%, Bond fund A provides an annual rate of return of 8%, Bond fund B provides an annual return of 9% and the money market fund provides an annual rate of return of 4%. The client wants to maximize return subject to the requirement that the total annual risk index be no more than $2.65 million. According to Vanguard'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 , each dollar invested in Bond fund B has a risk index of 0.48 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. Vanguard'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 bond funds must be within +/7% of the total amount invested in stocks. Formulate a Linear Programming model to determine optimal investment amounts