Friday, December 12, 2014

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...

Hello!


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 in bonds as and in funds as Then the domain is formed by...

Hello!


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 in bonds as and in funds as Then the domain is formed by the inequalities





or


They form a quadrilateral domain, please look at the picture given by the attached link. The function to maximize is




The line drawn in orange is The parallel line  touching the domain and with the greatest is the desired one.


It is evident from the picture that the point is the nearest to the orange line. This means $10 million should be invested in U.S. Treasury bonds and $30 million in mutual funds. The annual interest will be  3,000,000($).

No comments:

Post a Comment