A Las Vegas supermarket bakery must decide how many wedding cakes to prepare for the upcoming weekend. Cakes cost $26.68 each to make and they sell for $42.09 each. The price of unsold cakes is reduced to $17.86 on Mondays. Demand for the weekend is normally distributed with a mean of 70 and a standard deviation of 8.1.
What is the optimal probability of stocking out of wedding cakes on the weekend?