I'm trying to solve the apportionment problem in this image:
- There are four funds (F1, F2, F3 and F4) each with a fixed value.
- There are two people (P1 and P2) that need certain amounts of money.
- Each person can withdraw money from one or more funds but depending on the fund there is a maximum amount that can be taken.
The problem is to find one ore more solutions where all people receive the money they need.
I solved the problem programmatically but I'd like to know if there is a more elegant mathematical solution. I started with the idea of using a linear system of inequalities but I'm struggling defining it and I'm not even sure I'm on the right track (I'm not a mathematician).
I would greatly appreciate if someone could point me in the right direction.
Thank you in advance.
Alessandro