Store managers want an optimal inventory policy. Overstocking results in excessive storage and interest costs, whereas a small inventory means added costs for reordering and delivery. A supermarket manager estimates that a total of 800 cases of soup will be sold at a steady rate during the coming year and it costs $4 to store a case for a year. If he places several orders per year, each consisting of cases, then there will be an average of ½x cases in stock at any time and so storage costs for the year are (½x) 4 = 2x dollars. He also estimates that the handling cost for each delivery is $100. What is the optimal reorder quantity that minimizes costs?