The daily demand for printer cartridges in at an office supply store is N(30, 5). The cost of holding a roll in the store 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 cartridges 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 store given that the shortage probability cannot exceed .10.