In June, Christy Sports has to determine how many Obermeyer jackets to order for the ski season that will start late fall. Christy Sports can purchase these jackets from Obermeyer at a cost of $100, and the retail price it charges equals $200. Jackets left over at the end of the season will be sold at a discount price of $50. Christy Sports has to order jackets in multiples of 25. Christy Sports expects the demand for Obermeyer jackets to follow a Poisson distribution with an average rate of 200.

a. Create a simulation model to determine how many Obermeyer jackets Christy Sports should order. What is the optimal order quantity?
b. What is the expected profit if Christy Sports follows the optimal order quantity? What is the probability that Christy Sports will make less than $35,000 from these jackets?