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?
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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...
(The entire section contains 394 words.)
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