I have a set of integers $U$ with cardinality $311$ and whose sum is 500 dollars.
I want to group all the elements of this set into three different subsets:
The sum of the elements of subset $A$ is $450$ dollars.
The sum of the elements of subset $B$ is $30$ dollars.
The sum of the elements of subset $C$ is $20$ dollars.
What kind of algorithm could provide me a way to find the correct partitions?
What kind of tool could I use to find the vectors of solution? MS Excel is not capable of solving so many decision variables, even if they're integers. Thank you very much!