This is actually a quiz that will be needed in a real life food stall! I need to decide how much stock to supply for my pumpkin soup stall. I sell each soup for $5$ dollars a cup, and let's say my ingredients cost is $1$ dollar. Therefore an outcome of under-forecasting is $4$ dollars per unit, while an outcome of over-forecasting is 1 dollar per unit.
My forecast isn't so simple, however. I'm guessing that the most probable number of sales is $150$ units, but I'm very unsure, so there's a normal distribution behind this prediction with a standard deviation of $30$ units. This is harder than I expected.
Intuitively I would prepare ingredients for $180$ units, at which point I'd guess that the likely opportunity costs that would come with understocking would roughly meet the likely costs of overstocking. But given this is such a common dilemma, I thought that someone must be able to find a precise solution, and would then hopefully be able to explain it in layman's terms.