What is the Optimal Change Strategy for a Baker?

[Gerenuk]

Does anyone know results about how much and which bank notes a baker should have at the beginning of the day, to insure we will always be able to give proper change to customers?

Maybe the question could be:
Basically given a distribution of bank notes of the customers, what is the probability that the baker will have change for N deals?

 

[HallsofIvy]

That is not a mathematics question. It depends entirely upon what the bank's past experience has been.

 

[Gerenuk]

Then you haven't understood the question. I'm also talking about a baker and not a bank. It is probability theory and maybe combinatorics.

If every customer of the baker always pays with 100 euro bills, then the baker surely will run out of change quickly. If every customer pays in 10 cent coins, then everything is fine. So given the customers with a defined distribution of available notes (scaled to the prices of the bakery), which amount of small coins should the baker keep in order to be able to give change to all customers?