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 C₀ then the cost of placing all N  orders is: 

OC =  C₀N

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_n of this value:

The third component of total costs is simply the purchase cost of all the items, or . PC = pD =  Assuming that C₀, D, C_n and p are constant, what is the optimal order size q?