Consider an inventory system in which the sequence of events during each period is as follows:

(1) We observe the inventory level (call it i) at the beginning of the period.

(2) If i<= 1, 4 – i units are ordered. If I >= 2, 0 units are ordered.

(3) With probability 1/3, 0 units are demanded during the period;

a. With probability 1/3, 1 unit is demanded during the period; and

b. With probability 1/3, 2 units are demanded during the period.

(4) We observe the inventory level at the beginning of the next period.

Define a period’s state to be the period’s beginning inventory level. Determine the transition matrix that could be used to model this inventory system as a Markov chain.