Ashley has earmarked at most $270,000 for investment in three mutual funds: a money market fund, an international equity fund, and a growth-and-income fund. The money market fund has a rate of return of 6% per year, the international equity fund has a rate of return of 10% per year, and the growth-and-income fund has a rate of return of 16% per year. Ashley has stipulated that no more than 25% of her total portfolio should be in the growth-and-income fund and that no more than 50% of her total portfolio should be in the international equity fund. To maximize the return on her investment, how much should Ashley invest in each type of fund? A) Minimize P = 0.06x + 0.1y + 0.16z subject to x + y + z ≤ 270,000, y ≤ 135,000, z ≤ 67,5000, x ≥ 0, y ≥ 0, z ≥ 0 B) Maximize P = 0.06x + 0.1y + 0.16z subject to x + y + z ≤ 135,000, y ≤ 67,500, z ≤ 67,5000, x ≥ 0, y ≥ 0, z ≥ 0 C) Minimize P = 0.06x + 0.1y + 0.16z subject to x + y + z 0 D) Maximize P = 0.06x + 0.1y + 0.16z subject to x + y + z 0 E) Maximize P = 0.06x + 0.1y + 0.16z subject to x + y + z ≤ 270,000, y ≤ 135,000, z ≤ 67,5000, x ≥ 0, y ≥ 0, z ≥ 0

Question

Ashley has earmarked at most $270,000 for investment in three mutual funds: a money market fund, an international equity fund, and a growth-and-income fund. The money market fund has a rate of return of 6% per year, the international equity fund has a rate of return of 10% per year, and the growth-and-income fund has a rate of return of 16% per year. Ashley has stipulated that no more than 25% of her total portfolio should be in the growth-and-income fund and that no more than 50% of her total portfolio should be in the international equity fund. To maximize the return on her investment, how much should Ashley invest in each type of fund? A) Minimize P = 0.06x + 0.1y + 0.16z subject to x + y + z ≤ 270,000, y ≤ 135,000, z ≤ 67,5000, x ≥ 0, y ≥ 0, z ≥ 0 B) Maximize P = 0.06x + 0.1y + 0.16z subject to x + y + z ≤ 135,000, y ≤ 67,500, z ≤ 67,5000, x ≥ 0, y ≥ 0, z ≥ 0 C) Minimize P = 0.06x + 0.1y + 0.16z subject to x + y + z < 270,000, y < 135,000, z < 67,5000, x > 0, y > 0, z > 0 D) Maximize P = 0.06x + 0.1y + 0.16z subject to x + y + z < 270,000, y < 135,000, z < 67,5000, x > 0, y > 0, z > 0 E) Maximize P = 0.06x + 0.1y + 0.16z subject to x + y + z ≤ 270,000, y ≤ 135,000, z ≤ 67,5000, x ≥ 0, y ≥ 0, z ≥ 0

Quizplus · Accepted Answer

Ashley's goal is to maximize her return on investment, which is correctly represented by the objective function in option E. The constraints accurately reflect her stipulations regarding the total investment and the maximum percentages allowed in the international equity fund (50% of total, hence ≤ 135,000) and the growth-and-income fund (25% of total, hence ≤ 67,500). The constraints also correctly allow for the total investment to be up to $270,000 and ensure that investments in each fund are non-negative.

Ashley Has Earmarked at Most $270,000 for Investment in Three