EMERGENCY!!

OPERATIONS RESEARCH MARKOV CHAIN

please solve step by step

( 30 pts) Consider an inventory model in which the replenishment of stock takes place at the end of periods labelled n=0,1,2,, and we assume that the total demand for the single commodity during period n is a random variable Dn, independent of the time period. Assume that P{Dn=0}=.1,P{Dn =1}=.2,P{Dn=2}=.7. Assume that an (S,s) policy is used: If the end-of-period stock is less than or equal to s, then an amount sufficient to increase the quantity of stock on hand up to the level S is immediately ordered; otherwise, no new stock is ordered. Assume that S=2,s=1. Let Xn denote the quantity on hand at the end of period n, just before restocking. A negative value of Xn is interpreted as an unfilled demand that will be satisfied immediately upon restocking. This is the inventory example we studied in class; recall that {Xn,n>=0} is a Markov chain. Draw one-step transition matrix. (30 pts)