(25 points) In the basic EOQ model, suppose stock is replenished uniformly (rather than instantaneously) at the rate ofbitems per unit time until the order quantity Q is fulfilled. Withdrawals from the inventory are made at the rate ofaitems per unit time, whereab. Replenishments and withdrawals of the inventory are made simultaneously. For example, if Q is 60,bis 3 per day andais 2 per day, then 3 units of stock arrive each day for days 1 to 20, 31 to 50, and so on, whereas units are withdrawn at the rate of 2 per day every day. A diagram of inventory level versus time is given below for this example;

a) Find the total cost per unit time in term of the setup cost (K), production quantity (Q), unit cost (c), holding cost (h), withdrawal rateaand replenishment rateb. (Hint-compute the new holding cost per cycle)

b) Determine the economic order quantity, Q*.