Problem 2: Single-Period Inventory System (6 points)

A bakery makes fresh apple pies every morning. Demand for the pies is normally distributed with an average daily demand of 200 pies and a standard deviation of 63 pies. Pies are sold for $22 and it costs the bakery $8 to make each pie. If there are left over pies at the end of the day the local soup kitchen will buy them for $1 per pie, but the bakery estimates it costs $0.20 per pie to deliver the leftover pies to the soup kitchen.

1. What is the profit maximizing target service level? (3 points)
2. How many pies should the bakery make each morning to maximize its profit? (3 points)