A trust account client has $310,000 to be invested. The investment choices have current yields of 8%, 7%, and 10%. Suppose that the investment goal is to earn interest of $23,800.

(a) Find a general description for the amounts invested at the three rates. (Let x = the amount invested at 8%, y = the amount invested at 7%, and z = the amount invested at 10%. Express your answer in terms of z.) (x, y, z) =

( )

(b) If $10,000 is invested at 10%, how much should be invested at each of the other rates?

8%	$
7%	$

What if $30,000 is invested at 10%?

8%	$
7%	$

(c) What is the minimum amount that should be invested at 7%? $ In this case how much should be invested at the other rates?

8%	$
10%	$

(d) What is the maximum amount that should be invested at 7%? $ In this case how much should be invested at the other rates?

8%	$
10%	$