Optimizing Fund Allocation for Organization Expenses: A Real-World Math Problem

[Jboeding]

Hey everyone, I have a math problem that I need answered to solve an issue in the real world.

So, I am the treasurer of the Honors Student Council, an organization that looks after the Honors Program. We also have 10 Honors Societies.

We have been buying food for our giant meetings every Friday. Some organizations have more money than the other.

How would I get an event amount of money from each organization to pay back for the food according to their funds? I've been thinking percentages and stuff, but I have no idea how to do this, haha... or if it is even able to be executed.

Thank you everyone,
- Jacob

 

[MarkFL]

I have moved this thread, as it does not require calculus, but just some algebra to solve.

Suppose $T$ is the total cost that must be payed, and $p$ is the portion of each society's funds that should go to pay this cost. If $S$ is the sum of all the societies' funds, then we want:

$$pS=T\implies p=\frac{T}{S}$$

So, what you want to do is take the total cost, divide it by the total funds available, and then mutiply this resulting fraction by the funds of each individual society to get their share.

 

[Ackbach]

Although it might be considered more fair to go by the number of people from each society attending the Friday gatherings. If Honor Society A has twice as many people going to the gathering as all the others, they should pay twice as much. Presumably, the cost of the food is not a significant fraction of each society's total budget?

 

[MarkFL]

Although it might be considered more fair to go by the number of people from each society attending the Friday gatherings. If Honor Society A has twice as many people going to the gathering as all the others, they should pay twice as much. Presumably, the cost of the food is not a significant fraction of each society's total budget?

That's how I would actually charge each society, by their number of members rather than by their available funds. That would certainly be more equitable.

 

[Jboeding]

For all the math I've taken, it's quite sad I couldn't figure it out, haha.
(I'm curious if the guys in the math honor society could figure this out, :P).

As for the number of people v.s. the funds of each organization:
This meeting is just with the executive board members of each honor society/honor program, so we roughly have the same number of people per organization. Sorry, I should have clarified that. I agree with what you two are saying though, but some organizations have $0 - $7000, while the honor's program has $21,000.

Thanks for the help guys! I will be sure to give you guys credit when I bring this up next meeting :D!
- Jacob