Problema Solution
An investor has $24,000 to invest in bonds of AAA and B qualities. The AAA bonds yield an average of 6% and the B bonds yield 10%. The investor requires that at least three times as much money should be invested in AAA and B bonds.How much should be invested in each type of bond to maximize the return?
What is the maximum return?
Answer provided by our tutors
Let's define our decision variables. They will be:
Return
Point (.06x + .1y)
(0,0) 0
(24,000, 0) 1440
(18,000, 6000) 1680 This is the maximum return.
She should invest $18000 in AAA bonds & $6000 in B bonds.
Her return will be $1680.
x =
y =
What is our objective function?
The constraints are:
Graphing these will give us the feasible region. We can see that the feasible region is bounded. Where are the corner points?
Two of the corner points are obvious; they are: (0,0) and (24,000, 0). We must do a bit of
work to find the third corner point.
x = 3y and x + y = 24000 intersect where?
so (18,000, 6,000) is our third corner point. Let's evaluate the objective function.