Word Problem-6

Question

A pension fund manager decides to invest a total at most $25 million in US Treasury bonds paying 5% annual interest and in mutual funds paying 7% 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 $4000 on fes. How much should be invested in each to maximize annual interest? What is the maximum annual interest?

 

A. The amount that should be invested in Treasury bond is $_____million and the amount should be invested in mutual funds is $_______million.

Answer 1

You'll want to do this problem in the same way as the butterfat problem I answered earlier. I'll give you some hints, and see if you can use the other solution to go from there.

 

Let x be the amount (in millions) invested in T-bonds, and

Let y be the amount (in millions) invested in mutual funds.

 

If you invest x million dollars in T-bonds, you make 0.05x interest, and pay 100x in fees.

If you invest y million dollars in mutual funds, you make 0.07y interest, and pay 200y in fees.

 

Figure out which amounts are constraints, and what value you're trying to maximize, and go from there. Comment if you need some additional suggestions.