Consider a discrete-time, periodic review inventory model and let 6, be the total demand in period n, and let X,, be the inventory quantity on hand at the end-of-period n. An (s, S) inventory policy is used: If the endof-period stock is not greater than s, then a quantity is instantly procured to bring the level up to S. If the end-of-period stock exceeds s, then no replenishment takes place. (a) Suppose that s = 1, S = 4, and X0 = S = 4. If the period demands turn out to be 2,62 2, 2, what are the end-of-period stock levels X,, for periods n = 1, 2, ... , 8? (b) Suppose 6,, 62, . . . are independent random variables where Pr{6,,=0) =0.1,Pr(, = 1) =0.3,Pr{e,,=2} =0.3,Pr{6,,=3} = 116 III Markov Chains: Introduction 0.2, and Pr{,, = 4} = 0.1. Then X0, X . . . is a Markov chain. Determine P41 and P04