Beyer's sells winter coats, with most of the sales being made in the months of October, November, and December. Beyer's makes a one-time purchase of coats in September at a

cost of $40 each and sells each coat for S70. Any coats unsold at the end of December are marked down to $30 and sold in a special New Year's clearance sale. Any unsold coats always sell during the clearance sale. The following is the number of sales of coats for the past 10 years: 80, 100, 80, 110, 60, 90, 80, 80, 70, 90.Based on the observed 10 values of the prior demand, construct an empirical probability distribution of demand and determine the optimal number of coats for Beyer's to purchase based on the empirical distribution.