As a franchisee for Tiger Ice-Cream, you have a concession stand to sell ice-cream lollypops near campus. You can order as many of these lollypops from the franchisor as you want, delivered daily. You order them the day before, and they arrive first thing in the morning. The problem is: You do not know what your demand is going to be during the day. The number of customers arriving to you is a random number.
More importantly: You do not own a fridge – Ice Creams you do not sell will melt and you will need to dispose. Your Wholesale Price is c = $1 per lollypop, and you sell them at the Retail Price of p = $3 per lollypop. Tiger Ice-Cream controls these prices, not you.
You are told that total demanded quantity any given day is a Normal random variable with mean 997 units, and standard deviation 10 units.
If the lollypops you do not sell are worthless to you, how many units should you order the night before, if your objective is to maximize your expected profits?