# math - linear programming

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A woman wishes to invest \$12,000 in three of bonds: municipal bonds paying 7% interest per year, bank investment certificates paying 8%, and high-risk 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 high-risk bonds will be 12,000 – x – y]. Hence, suppose the investor decides to increase the maximum invested in high-risk bonds to \$3000 but leaves the other conditions unchanged. By how much will her maximum possible interest yield increase?

• math - linear programming -

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.