1. Lucy Lindner owns a small campus bookstore that sells UC sportswear. In February, she must place an order with Nike for a new UC football shirt for the coming season. The long lead time is required for the contract manufacturers in Asia to order the necessary materials and to begin production in April. The shirts will be delivered to Lucy in early August just in time for the new season. Nike will charge Lucy $50 for each shirt she orders, and she will sell each shirt for $75 during the football season. There will not be another opportunity for Lucy to order any more shirts if she runs out. At the end of the season, Lucy will sell all the shirts that are left at a price of $15. Obviously, Lucy doesnt know exactly what the demand for these shirts will be, but during the past few years she has sold an average of 500 shirts each season that are similar to this new shirt. Based on historical sales the

   demand for the shirts appears to be normally distributed with a standard deviation of 75, and Lucy is planning to order 550 shirts this year. Develop a simulation model for this problem using Python in a Jupyter Notebook. Generate a simulation sample of 10,000 trials and use it to answer the questions below.

   a. Describe the distribution of Lucys total profit for this order? b. What is the mean total profit for this order? c. What is the probability that Lucy will incur a net loss on this order? d. What is the order quantity that maximizes Lucys mean total profit?