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## Homework Statement

This is not a homework question, but it is something I want to work on related to something I volunteer for. Regardless, I did not know where to post this question and this forum was the best place I could think of it. I don't need someone to work it out for me, but what I am looking for is to be pointed in the right direction.

The question is as follows:

I have n people and over the course of about 30 weeks, there are m classes. Sometimes in a week there are 2-3, sometimes in a week there are none. Classes can have between 5-25 people in them depending on their type, but all that matters for the question at hand is that classes have a limit on how many people they can have, and this limit varies from class to class.

For the ENTIRE 30 WEEKS, people have placed preferences for whether they would like to be in a class or doing a completely separate activity, by week.

The best possible solution is where as many people are in these classes and that everyone is in the same number (i.e. you don't have some in 7 classes and others in 2, I'm looking for a nice even spread).

## Homework Equations

I think this section is explained above...

## The Attempt at a Solution

I note this seems to be somewhat like a Linear Programming question, and half of a subject I did at university was on LPs. But it was a year ago now since I did it and this is quite a specific type. Things like Simplex method and Interior Point method race through my mind but I don't know lol.

I searched this on google which was helpful at getting me clearer but the best things I could come across were things like the Assignment problem or the Stable Marriage problem (can't link them as I am under 10 posts)

I am fairly sure it is an LP, what I am looking for is where to go from here. I know this is my first post in this forum so I really hope I posted this in the right place - I read the stickies. To me this seems to be a fairly complex problem, so if someone doesn't know how to help but can still tell me a good place I could re-ask this question, that would be AWESOME.