let

x = the money invested in AAA bonds, x=> 0

y = the money invested in B bonds, y =>0

an investor has $24,000 to invest in AAA and B Bonds

x + y <= 24000

the investor wants to have at least three times as much money in the AAA bonds as in the B Bonds

x => 3y

we will define the return by

F(x , y) = 0.06x + 0.10*y (the objective function)

lets draw the graph of the system of inequalities (constrains) and determine the corner points

x=> 0

y => 0

x + y <= 24000

x =< 3y

click here to see the graph

Click to see all the steps

there are 3 corner points and we calculate F(x ,y) for each point to find the maximum value (the biggest value for F):

(0, 0) => F(x , y) = $0

(24000, 0) => F(24000, 0) = 0.06*24000 = $1440

by solving the system we find the third corner point

x = 3y

x + y = 24000

click here to see the step by step solution of the system of equations

Click to see all the steps

x = 18000

y = 6000

F(18000, 6000) = 0.06*18000 + 0.10*6000 = $1680 this is the maximum return

To maximize the return $18,000 should be invested in AAA bonds and $6,000 in B bonds.

The maximum return equals $1,680.