Given a product that costs $4.38 per unit and has an average lead time of 12 days, standard deviation of lead time of 3 days, average demand of 36.1 units/day, standard deviation of demand of 25.9 units/day, stockout cost of $0.25 per unit, ordering cost of $30/order, inventory holding cost of 20% of item cost and needs to be in-stock 90% during lead time, calculate the following (you can leave all of these as decimals):
a) Economic order quantity.
b) Expected number of units out of stock during an order cycle
c) Average time between orders. Answer must be shown in days.
d) Average inventory level.
e) Reorder point.