Please answer these questions in the text box below. All questions share the same context. Please write down the Excel or mathematical formula and the calculated result, keeping a few significant digits. For example: SQRT(10)=3.16. You may also accompany your answers with brief explanations for ease of understanding.

1. An oyster bar serves an average of 1,000 oysters per day. The purchase cost is roughly $2 each. Because oysters must be kept on ice and there is heavy spoilage over night, the daily inventory holding cost is estimated to be 45% (i.e., it costs on average $0.9 to keep an oyster in storage for a whole day). The delivery cost per order is $50. How many deliveries per day are optimal for the oyster bar to minimize total costs?

(Hint: the EOQ formula in the lecture is provided based on the time unit of a year, but the formula actually applies to any time unit as long as it is consistently used for all parameters. Therefore, you can plug in the demand per day and the inventory holding cost percentage per day and the formula still yields the correct optimal order quantity.)

2. Suppose the oyster bar operates 10 hours a day and thus the average consumption rate is 100 oyster per hour, however due to demand fluctuation the bar determines it should keep a safety stock of 30 oyster. Suppose the oyster supplier's lead-time (from order to delivery) is 1.5 hours. If the inventory is constantly monitored, when the inventory drops to what level (reorder point) should the oyster bar makes another order? If the demand becomes more variable over time (but unchanged on average), should the reorder point become higher or lower?

(Hint: the reorder point in the lecture P = LR/250 really means "L days worth of demand" given the lead time being L days yet the demand R is per year, where 250 is the estimated number of working days in a year. In this problem, both demand and lead time are measured in hours, so the reorder point should represent "L hours worth of demand" which is P = LR; there is no need for the division by 250 because there is no conversion of time units. In addition, this is the reorder point formula assuming stable demand. With stochastic demand, the reorder point should be raised by an amount to provide a buffer for temporarily increased demand, namely safety stock.)