math  linear programming
posted by Sky on .
A woman wishes to invest $12,000 in three of bonds: municipal bonds paying 7% interest per year, bank investment certificates paying 8%, and highrisk bonds paying 12%. For tax reasons she wants the amount invested in municipal bonds to be at least three times the amount invested in bank certificates. To keep her level of risk manageable, she will invest no more than $2000 in high risk bonds. How much should she invest in each type of bond to maximize her annual interest yield? [Hint: Let x = amount in municipal bonds and y = amount in bank certificates. Then the amount in highrisk bonds will be 12,000 – x – y]. Hence, suppose the investor decides to increase the maximum invested in highrisk bonds to $3000 but leaves the other conditions unchanged. By how much will her maximum possible interest yield increase?
please help me find the equation, contraints and the answer.....
please and thank you..

If the 3 amounts are x,y,z for 7%,8%,12% respectively, then we want to
maximize .07x + .08y + .12z subject to
x+y+z = 12000
x >= 3z
z <= 2000
use your favorite tool to calculate the result.