Mr. Tran has $24,000 to invest, some in bonds and the rest in stocks. He has decided that the
money invested in bonds must be at least twice as much as that in stocks. But the money invested
in bonds must not be greater than $18,000. If the bonds earn 6%, and the stocks earn 8%, how
much money should he invest in each to maximize profit?
Stocks earn 8%, while bonds earn only 6%.
Therefore, wishing maximize the interest, the most agressive strategy is to invest
as much in stocks as possible under the imposed rstrictions.
The restriction "the money invested in bonds must not be greater than $18,000"
does not limit the investment amount in stokcs from the upper side,
so we can ignore it: it is not a working restriction in this problem.
The other restriction is that "the money invested in bonds must be at least twice
as much as that in stocks".
In this problem, it means that the maximum investment in stocks is $8000,
leaving $24000 - $8000 = $16000 to invest in bonds.
ANSWER. Under given conditions, $8000 should be invested in stocks
and $16000 should be invested in bonds to maximize the annual interest.