A small car dealer, who is eager to estimate his inventory cost,can hold up
to 4 cars in the showroom. The periodic demand for the cars isfollowing a Poisson
distribution with mean 2, except for the maximum inventory level.In the case of
maximum inventory level, the dealer makes a special discount byoffering a price much
below the market which results in depletion of its entireinventory. Once all the cars are
sold, the dealer immediately orders 3 or 4 cars with equally likelyprobabilities. Apart
from maximum and minimum inventory levels, the dealer can sell allhis cars and also
seek to refill its inventory. The Inventory cost is given as; $500per car per period.
(a) Construct the transition probability matrix, by properlydefining the states and the
state space.
(b) Find the average inventory holding cost per period.
