Consider the inventory control problem environment mentioned in class. The inventory policy considered is different than the one mentioned in class and is as follows: o If there is one camera or less in stock at the end of Saturday, then you order 3 cameras. o If there are two or more cameras in stock at the end of Saturday, then you do not order at all. The orders you give at the end of Saturday arrive to the store early on Monday. When a customer demands the product in a particular week, if the cameras are out of stock then you lose that customer. The state, is defined as the number of items in the inventory at the end of week n. represents the demand in period , a random variable. The distribution of demand is stationary in time and is specified by a discrete uniform distribution in the range [0, 4].

a. Form a Markov chain to model this situation.

b. Does the formulated Markov chain in part-a have a steady state distribution? If so, determine the steady state probabilities.

c. Given that the current inventory level (at time 0) is 2, what is the probability of ending up with nonzero inventory level in period 2 (at time 2)?

d. If the initial inventory level is not known, but it is known that it is equally likely to start with 2 or 3 units on hand, what would be the answer of the previous question?

e. Consider the following cost structure:

o There is fixed ordering cost of 10TL per order and additional cost of 8 TL per unit ordered.

o For every demand satisfied, revenue of 20TL is obtained.

o There is an inventory carrying cost of 3TL/unit for each unit on hand at the end of the period.

o There is a fixed lost sale cost of 25TL if two or more customers are lost in the same period.

Compute the long-run average income per period.Consider the inventory control problem environment mentioned in class.