An investor has at most $90,000 to invest in government bonds, mutual funds, and money market funds. The average yields for the government bonds, mu
market funds are 6%, 8%, and
7% respectively. The investor's policy requires that the total amount invested in mutual and money market funds not exceed
the amount invested in
government bonds. How much should
be invested in each type of investment in order to maximize
the return? What is the maximum return in the first year
?
How much should be invested in government bonds?

You want to know how to invest a total of $90,000 among government bonds, mutual funds, and money market funds earning 6%, 8%, and 7%, respectively, if the total in mutual and money market funds does not exceed the amount in government bonds.

Setup

Let b, m, k represent the amounts invested in bonds, mutual funds, and money market funds, respectively. The given constraints tell us ...

b + m + k ≤ 90,000

m + k ≤ b

and we want to maximize ...

0.06b +0.08m +0.07k

Solution

Rewriting the first equation, we have ...

b ≤ 90000 -m -k

Using that with the constraint provided by the second equation, we have ...

m +k ≤ b ≤ 90000 -m -k

Ignoring b for the moment, we can write this as ...

m +k ≤ 90000 -m -k

Adding (m+k) to both sides, we have ...

2(m +k) ≤ 90000

m +k ≤ 45000

Yield

To maximize the return, we need to maximize the investment in the product(s) that give the highest return. Of mutual funds (m) and money market funds (k), the one with the highest return is mutual funds.

That means we want to choose m = 45000.

This results in b ≤ 90000 -45000 = 45000.

The return will be ...

0.06(45000) +0.08(45000) +0.07(0) = (0.14)(45000) = 6300.

The investment amounts should be ...

$45000 in government bonds
$45000 in mutual funds
$0 in money market funds

for a return of $6300 in the first year.

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Additional comment

This is a math problem, not investment advice.