Consider a periodic review inventory system operating under an order-up-to (base stock) policy where unsatisfied demand is backordered. Assume that Demand in period t, Dt is an alternating stochastic process with the following structure. In odd-numbered periods (t = 1, 3, 5...), it is independent and normally distributed with mean Mo and standard deviation o o and in even numbered periods (t = 2, 4, 6...), it is independent and normally distributed with mean Me and standard deviation o e. Assume that the order-up-to level is Q=10 which is also the initial inventory level lo = 40. a. (4 points) Assuming that the lead time is zero (orders given at the end of period t are received in the beginning of period t +1), write the inventory dynamics for the first four periods (expressit the inventory level at the end of period t and the order quantity O t). Explain and justify your reasoning. b. (4 points) Find E[l 15], the expected inventory level at the end of period 15 (explain and justify your reasoning). C. (5 points) Find Var[l 15), the variance of the inventory level at the end of period 15 (explain and justify your reasoning). d. (6 points) Now assume that the lead time is 1 period, find Var[115], the variance of the inventory level at the end of period 15 (explain and justify your reasoning). Consider a periodic review inventory system operating under an order-up-to (base stock) policy where unsatisfied demand is backordered. Assume that Demand in period t, Dt is an alternating stochastic process with the following structure. In odd-numbered periods (t = 1, 3, 5...), it is independent and normally distributed with mean Mo and standard deviation o o and in even numbered periods (t = 2, 4, 6...), it is independent and normally distributed with mean Me and standard deviation o e. Assume that the order-up-to level is Q=10 which is also the initial inventory level lo = 40. a. (4 points) Assuming that the lead time is zero (orders given at the end of period t are received in the beginning of period t +1), write the inventory dynamics for the first four periods (expressit the inventory level at the end of period t and the order quantity O t). Explain and justify your reasoning. b. (4 points) Find E[l 15], the expected inventory level at the end of period 15 (explain and justify your reasoning). C. (5 points) Find Var[l 15), the variance of the inventory level at the end of period 15 (explain and justify your reasoning). d. (6 points) Now assume that the lead time is 1 period, find Var[115], the variance of the inventory level at the end of period 15 (explain and justify your reasoning)