A small copy center uses five 500-sheet boxes of copy paper a week. Experience suggests that usage can be well approximated by a normal distribution with a mean of five boxes per week and a standard deviation of one-half box per week. Two weeks are required to fill an order for letterhead stationery. Ordering cost is $ 2, and annual holding cost is 20 cents per box.
a. Determine the economic order quantity, assuming a 52-week year.
b. If the copy center reorders when the supply on hand is 12 boxes, compute the risk of a stockout.
c. If a fixed interval of seven weeks instead of an ROP is used for reordering, what risk does the copy center incur that it will run out of stationery before this order arrives if it orders 36 boxes when the amount on hand is 12 boxes?