Question

An investor has up to $450,000 to invest in two types of investment. Types A pays 6% annually and type B pays 10% annually. To have a well-balanced portfolio, the investor imposes the following conditions. At least one-half of the total portfolios is to be allocated to type A investments and at least one-fourth of the portfolio is to be allocated to type B investments. What is the optimal amount that should be invested in each type of investment? What is the optimal return?

Answer 1

maximize p = .06x + .10y subject to
x+y <= 450000
x >= y
y >= x/3

maximum p=36000 occurs when x=y=22500