A Las Vegas supermarket bakery must decide how many wedding cakes to prepare for the upcoming weekend. Cakes cost $50 each to make and they sell for $90 each. The price of leftover wedding cakes is reduced by 50% on Mondays to clear out inventory. Demand for the weekend is normally distributed with a mean of 109 and a standard deviation of 28. What is the optimal number of wedding cakes to stock on the weekend? Carry answer to 4 decimal palces.