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?
Start with the given facts (in millions of dollars).
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.