You run a small, local fishery. You contract local fishermen to sell you their fish in bulk, and then turn the fish around to sell at a profit.

Through years of data collection you've managed to decide that your average demand for pounds of fish per day looks approximately Poisson, with a mean of 100 pounds of fish sold per day.

Your existing deal with the fishermen says that you'll buy from them at a fixed rate of S6.00 per pound, while you can turn that around and get $9.99 per pound from a nearby market.

Nobody will buy yesterday's fish from a fish market, so you've contacted a regional cannery and they will buy your unsold fish at the end of the day at a flat rate of $1.00 per pound.

How much fish should you buy from the locals every day to maximize profit?

Make sure to run more than one simulation, and your recommendation may take some guessing!