A pension fund manager decides to invest a total of at most $40 million in U.S. Treasury bonds paying 6% 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 $40 million in U.S. Treasury bonds paying 6% annual interest and in mutual funds paying 8% annual interest. He plans to invest at least $5 million in bonds and at least $20 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 $7000 on fees. How much should be invested in each to maximize annual interest? What is the maximum interest?

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Borys Shumyatskiy eNotes educator | Certified Educator

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Such problems are called linear programming ones. We have a two-dimensional domain formed by straight lines, and a linear function to maximize on this domain. To solve such a problem it is desirable to draw the domain and a line where the function to maximize has some value (all such lines are parallel).

Denote a number of millions invested...

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