Katadyn purchases 8,000 filters each year as components of their portable hiking water filters. The unit cost of each filter is $10, and the cost of carrying one filter in inventory for a year is $3. Ordering cost is $30 per order.
What are (a) the optimal order quantity, (b) the expected number of orders placed each year, and (c) the expected time between orders? Assume that Katadyn operates on a 200-day working year.