Lets say I have a swimming pool filled with differently coloured balls. There are a fixed number of different colours. Each differently coloured ball has set cost (not necessarily unique) that I don't know.
I can take as many random samples of the pool as required (e.g. I can fill 1000 bags with 100 randomly sampled balls from the pool). I know the total cost of each bag and how many balls of each colour there are in each bag.
How can I determine the cost for each ball colour?
(Apologies in advance if I didn't put the correct tag, math newb here - corrections are most welcome)