Question

formulate but do not solve the following exercise as a linear programming problem. ashley has earmarked at most $210,000 for investment in three mutual funds: x dollars in a money - market fund, y dollars in an international equity fund, and z dollars in a growth - and - income fund. the money market fund has a rate of return 5%/year, the international equity fund has a rate of return of 10%/year, and the growth - and - income fund has a rate of return of 14%/year. ashley has stipulated that no more than 30% of her total portfolio should be in the growth - and - income fund and that no more than 45% of her total portfolio should be in the international equity fund. to maximize the return on her investment p (in dollars), how much should ashley invest in each type of fund? maximize p = subject to the constraints total investments growth - and - income percentage international equity percentage x≥0 y≥0 z≥0 resources read it watch it show my work (optional)

Explanation:

Step1: Define the objective function

The return on the money - market fund is $0.05x$, on the international equity fund is $0.1y$, and on the growth - and - income fund is $0.14z$. So the objective function to maximize is $P = 0.05x+0.1y + 0.14z$.

Step2: Set the total investment constraint

Ashley has earmarked at most $210000$ for investment. So $x + y+z\leqslant210000$.

Step3: Set the growth - and - income percentage constraint

No more than 30% of her total portfolio should be in the growth - and - income fund. So $z\leqslant0.3(x + y+z)$.

Step4: Set the international equity percentage constraint

No more than 45% of her total portfolio should be in the international equity fund. So $y\leqslant0.45(x + y+z)$.

Answer:

Maximize $P=0.05x + 0.1y+0.14z$
subject to the constraints:
$x + y + z\leqslant210000$
$z\leqslant0.3(x + y+z)$
$y\leqslant0.45(x + y+z)$
$x\geqslant0,y\geqslant0,z\geqslant0$