The daily demand for camera films at a gift shop is N(300, 5). The cost of holding a roll in the shop is $.02 per day, and the fixed cost of placing a replenishment order is $30.

The shop’s inventory policy is to order 150 rolls whenever the inventory level drops to 80 units. It simultaneously maintains a buffer of 20 rolls at all times.

(a) Determine the probability of running out of stock.

(b) Given the data of the situation, recommend an inventory policy for the shop given that the shortage probability cannot exceed .10.