A pension fund manager decides to invest a total of at most $30 million in U. Treasury bonds paying 3% annual interest and in mutual funds paying 5%...

 A pension fund manager decides to invest a total of at most ​$30 million in U.S. Treasury bonds paying 3​% annual interest and in mutual funds paying 5% annual interest. He plans to invest at least ​$5 million in bonds and at least ​$10 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 ​$5000 on fees. How much should be invested in each to maximize annual​ interest? What is the maximum annual​ interest?