Question

If you provide a handwritten answer please make sure it is legible!  Thanks!

An investor has at most ​$90,000 to invest in government​ bonds, mutual​ funds, and money market funds. The average yields for government​ bonds, mutual​ funds, and money market funds are 7%, 8​%, and 12% 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?

Answer 1

As per the given information above, we can summarize as under:

b = bonds
m = mutual funds
f = money market funds
So, b + m + f = $90000
m + f = b
Profit = 0.07b + 0.08m + 0.12f

The investor should invest in that where he is getting maximum return which in this case is money market funds, as there is no mandate to be in all three investment types. Thus, to maximize yields the investor should put as much as he can in money market funds, which pays 12% the highest amount. Since mutual funds and money market funds cannot exceed the amount in government bonds,
Then, the maximum return is $45000 in money market, and the other $45000 in government bonds, but nothing in the mutual funds.
Government= $45000
Money Market = $45000

Yield = 0.07 (45000) + 0.08 (0) + 0.12 (45000)
= $3150 + $5400
= $8550

Thus, $8550 is the maximum return in the first year.