A Fashionable Job

In an unexpected twist of events, you recently inherited a high-end fashion goods store, Elite Couture, from a distant relative. You are looking forward to apply your extensive knowledge of Operations principles to this store.

Your first challenge is to decide on the quantity of Luella Bartley handbags to sell during the summer season. The unit cost of the handbag is 28.50 and the handbag sells for 150. All handbags remaining unsold at the end of the season are purchased by a discounter for 20 each. Further, there is a significant 40% inventory holding cost incurred for each unsold bag. Demand for bags is distributed normally with mean 150 and standard deviation 20.

How many bags should be purchased to maximize expected profit?