# How Much Should I Make?

A little background: I thought about this problem yesterday, while I was helping a friend out at a particular competitive event where he was to cook a certain amount of food for guests, who would then vote for a winner. At this particular event, there were 450 guests being served by 15 food vendors (where my friend was 1 of the 15). The timespan of the event was 3 hours.

Now, the coordinators of the event told every vendor to make exactly 450 meals (it was a sandwich competition, so the meals were small sandwiches). This is obviously way to much; few people can eat 15 different meals in 3 hours. The more popular vendors will sell more than the less popular ones, however, for the sake of the problem, assume that each vendor is equally as popular as the next.

My question is this: 450 people attend an event. Each person eats at least one meal, with the maximum being 15 meals (no one is going to eat more than 15, because once they hit 15 they will have tried everything and thus know who to vote for). 15 vendors serve food to the 450 people at the event. How much should each vendor make in order to sell out (and thus not get stuck with a ton of leftovers)?

Extra info: My friend obviously did not sell out, and got stuck with a ton of leftovers. I think we sold around 150 sandwiches. Is the answer around 150-200? Just a rough guess. I really don't know how to solve it, or if there is even enough information to solve it, but was interested in the answer.

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