A major component of the costs of many large firms is the cost associated with ordering and holding inventory. If the yearly demand for the good is D and the size of each order placed is  q  then the number of orders  N  in each year is:

N=D/Q

If the cost of placing each order is C_o then the cost of placing all N orders is:

OC = C_oN

The second component is the carrying or handling cost of an inventory. Under the assumption that the average number of items in stock is q / 2  and with cost of each item set at  p , the value of this average number of items is p (q / 2) . The carrying in this situation is the proportion C of this value:

CC = C_np (q/2)

The third component of total costs is simply the purchase cost of all the items, or PC = pD.  Assuming that C_o, D, C_n and p are constant, what is the optimal order size q?