undefined

4. Consider the inventory problem with demand having the following probability distribution: P{D=0}=1/4, P{D=1}=1/4, P{D=2}=1/2, P{D>=3}=0 The ordering policy now is changed to ordering just 2 cameras at the end of the week if none are in stock. As before, no order is placed if there are any cameras in stock. Assume that there is one camera in stock at the time (the end of a week) the policy is instituted. a) Construct the (one-step) transition matrix. (5 pts) b) Find the ij (the expected first passage time from state i to statej) for all i andj. (20 pts) c) Find the steady-state probabilities of the state of this Markov chain. (12 pts) d) Assuming that the store pays a storage cost for each camera remaining on the shelf at the end of the week according to the C(O)=$0, C(1)=$2 C(2)=58, find the long run expected average storage cost per week. (7 pts)