1. An automaker buys a certain part to assemble the transmission. The supplier charges a price of $8 per part for quantities of 600 part or more, $9 per part for orders of 400 to 599 parts, and $10 per part for lesser quantities. The automaker operates 200 days per year. The automaker needs 25 parts per day, and ordering costs are $48. Holding costs are $2 per year for each part, what is the order quantity that will minimize total annual cost.
2. La Poire sells artisan European style cake. Demand varies uniformly between 300 cakes and 500 cakes per day. It costs La Poire $10 to make a cake. La Poire sells each cake for $25. La Poire gives a 75% discount for its cake at the end of the day. Find the optimal stocking level that maximizes expected profit for La Poire and its stockout risk for that quantity.