Herman operates an independent hardware store that sells a large number of stock keeping units. One of these is a high-end window air conditioning unit that Herman buys for $485 and sells for $880. Because these products are manufactured in Thailand, Herman has to place a single order 10 weeks before the selling season. He has no opportunity to replenish inventory after the initial order. At the end of the season, Herman can sell any remaining units to an overstock warehouse for $400 each. Based on sales from previous years, he estimates that demand during the season is normally distributed with a mean of 3,400 units and a standard deviation of 1,247 units.

1. How many of these air conditioners should Herman order from the manufacturer?

2. If Herman orders the quantity you recommended in part (a), what would be the probability that he will stock out of this item?

3. Herman was frustrated last year because a cool summer meant that sales were lower than anticipated. Not wanting to face this problem again, he was planning to use an order quantity of 3,300. In the process of convincing him to use your optimal order quantity from part (a), you want to show him the service level that he would achieve if he used 3,300 as his order quantity. What is this service level?

4. The manufacturer is thinking of offering the following scheme to Herman. At the end of the season, they will buy back unsold air conditioners at a price equal to Hermans original cost ($485) less $50. However, Herman would have to bear the costs of shipping the units back to the manufacturer at a cost of $20 each. What is the quantity that Herman should order under this new scheme? Are consumers better off with this arrangement? Is Herman better off?