A retailer store has to decide how many t-shirts of a particular kind to order for the season. The anticipated demand is normally distributed with a mean of μ = 800 and a standard deviation of σ = 200. Each t-shirt costs $15 to acquire and the introductory sale price is to be $60. Any unsold units at the end of the season are unlikely to be very valuable and will be disposed of in a sale for $10 each. It costs $5to hold a unit in inventory for the entire season.

1. What is the cost of understocking and overstocking by one unit? What is the optimal cycle service level?
2. How many units should be acquired for sale?
3. What is the expected profit?
4. How many t-shirts on average will have to be disposed off in the sale at the end of the season?