Question

A pension fund manager decides to invest a total of at most ​$30 million in U.S. Treasury bonds paying 6​% annual interest and in mutual funds paying 9​% 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?

Answer 1

The goal here is to invest as much in mutual funds as possible while keeping the fees under $5000 because mutual funds pay more interest.

If $30 million mutual, fees = (30*200)=6000

Each one million dollar that we shift from mutual funds to treasury will result in a $100 reduction in fees

For Example 29 million in mutual fund, 1 million in treasury, fee= (29*200)+100=5900

So in order to get the fees down to 5000 we have to invest $10 million in treasury and $20 million in mutual funds, this will maximize our interest income while keeping fees less than $5000

(20 *200)+(10*100)=5000

Step-by-step explanation: