# 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 alllowed to spend no more than \$6000 on fees. How much should be invested in each to maximize annual interest?

Jedidiah Hahn | Certified Educator

calendarEducator since 2012

starTop subjects are Math and Science

Let x be the amount in millions dollar invested in bonds paying 5% annual interest. And let y be the amount in million dollars invested in mutual funds paying 8% annual interest.

Then, determine the constraints for each given conditions.

For the first condtion, the manager decides to invest a total of at most \$35 millions. So, its equivalent equation is:

`x + y lt= 35`

Next, he plans to invest at least \$5 million in bonds and at least \$15 millions in mutual funds. So, the equivalent equations are:

`x gt= 5`

`ygt=15`

Also, the manager is allowed to spend no more that \$6000 on fees. Since the initial fees for bonds is \$100 per million dollars and for mutual funds \$200 per million, then its equation is:

`100x + 200y lt= 6000`

And this simplifies to:

`x + 2y lt=60`

Hence, we have four constraints. These...

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