Suppose a company requires N units per year of a certain commodity. Suppose further that it costs D dollars to order a shipment of the commodity and that the storage cost per unit is S dollars per year. The units are used (or sold) at a constant rate throughout the year, and each shipment is used up just as a new shipment arrives.

a. Show that the total cost C(x) of maintaining inventory when x units are ordered in each shipment is minimized when x = Q where

b. The optimum order size Q found in part (a) is called the economic order quantity (EOQ). What is the EOQ when 9,720 units per year are ordered with an ordering cost of $35 per shipment and a storage cost of 84 cents per unit per year?

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Q(N, D, S) = 2DN S