You have been tasked with figuring out what the optimal percentage of understock is during lead time. Your boss is still miffed about stocking out 50%. You have figured out the following data:

The cost of your product is $2,952

You sell your product for $4,141

When you stock out, your customers get upset and buy from your competitor for a little while. Your competitor is terrible so your customers always come back eventually. You figure that the typical unhappy customer orders from your competitor 1 times; so, you lose the value of 1 sales of your product to that customer before she or he comes back and starts buying again.

If you have inventory left at the end of lead time that material doesn't really have to be discounted because it's still good and you'll just sell it. But you do figure that you incurred some cost of having too many in inventory. You estimate that your cost of holding one unit too many is about 0.021 of the product's cost.

Calculate the optimal probability of not stocking out during lead time (a.k.a, probability that demand is less than your quantity of inventory).