Consider a product which is produced in two consecutive machines. The demand rate, 1, is constant and continuous. The production rate in the first machine is 41, and in the second machine 21. A batch is placed in front of the first machine. Units that have left machine 1 are immediately processed in machine 2. When the whole batch has gone through both machines it is sent to a warehouse facing the continuous constant demand. The setup costs in the machines are Ky and K2. The unit costs are c before machine 1, c2 between the machines, and C3 after machine 2. The holding cost rate is i per dollar per year. (a) Draw the inventory level versus time graph for two cycles for (i) items before machine 1, (ii) items between machines 1 and 2, and (iii)items after machine 2. (b) Derive the corresponding total cost per unit time. (c) Determine the optimal batch quantity