Linear Programming  Math
posted by Geen .
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 wellbalanced portfolio, the investor imposes the following conditions. At least onehalf of the total portfolios is to be allocated to type A investments and at least onefourth 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?

maximize p = .06x + .10y subject to
x+y <= 450000
x >= y
y >= x/3
maximum p=36000 occurs when x=y=22500