# A pension fund manager decides to invest a total of at most \$35 million in U.S treasury bonds paying 5% annual interest and in mutual funds paying 8% annual interest. He plans to invest at least \$5...

A pension fund manager decides to invest a total of at most \$35 million in U.S treasury bonds paying 5% annual interest and in mutual funds paying 8% annual interest. He plans to invest at least \$5 million in bonds and at least \$15 million in mutual funds. Bonds have an initial fee of \$100 per million dollars, while the fee for mutual funds is \$200 per million. The fund manager is allowed to spend no more than \$6000 on fees. How much should be invested in each to maximize annual interest?

durbanville | Certified Educator

Let `x =` Treasury bonds and let `y=` Mutual funds:

`xgt=5` and `ygt=15`

We also know that `0.0001x+0.0002ylt=0.006` so to make it easier to work with we can say that  (cost)`x` +(cost)2y <=60 (times \$100) because we spend \$100 per \$1m on treasury(`x` ) and \$200 per \$1m on Mutual funds (`y` ).

To maximize he needs to spend all his money within his restrictions.

When (cost)x=\$100 and (cost)y=\$200 `therefore 10x +25y = \$6000`

Therefore he should invest \$10 million in Treasury bonds @5% annual interest and \$25 million in Mutual funds @ 8% in order to maximize annual interest in the first year.