Question

An investor has up to $650,000 to invest in two types of investments. Type A pays 13% annually and type B pays 7% annually. To have a well-balanced portfolio, the investor imposes the following conditions. At least one-half of the total portfolio is to be allocated to type A investments and at least one-fourth is to be allocated to type B investments. What is the optimal amount that should be invested in each type of investment?

Answer 1

If the amounts in A and B are x and y, then (suppressing all the extra zeros),

maximize p=.13x+.07y subject to
x >= 65/2
y >= 65/4
x+y <= 65

Now use your favorite tool to solve. A good one is at

http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html