Consider the following extension of the EOQ model, often labeled economic manufacturing quantity (EMQ). Most of the assumptions of the EOQ and EMQ models are the same, but in the latter, rather than assuming instantaneous replenishment of inventory, inventory is replenished at production rate p, which gives the number of parts produced per unit time. Find the order quantity minimizing the sum of inventory and ordering cost, averaged over time. (Hint: Draw the inventory level during an ordering cycle.)