Can you help me solve this question? Thank you so much!

_ _ Consider the following inventory problem. A camera store stocks a particular model camera that can be ordered weekly. Let D\" be the demand of the camera in the nth week. Assume {Du }=1 are independent and identically distributed random variables and have the following probability mass function _Ii--E-E- Let X be the inventory level at the end of week 1:. Suppose X0 = 3. The ordering policy is as follows. If X\" S 1, then order up to 3. For example, if X,| =1, meaning there are only 1 items in the store at the end of week 71., then order 2 items over the weekend so that next Monday morning there are 3 items in the store (i.e. there are 3 items in the beginning of week n + 1). If X" 2 2, do not order. (a) It can be shown that {Xn : n 2 0} is a discrete time Markov chain. Please write down the transition matrix. (b) Suppose the storage cost for holding the camera on hand is 0(0) = 0,0(1) = 2, 0(2) = 6, 0(3) = 12. Then what is the long-run expected average cost per unit time for the store