An office supply store keeps a small inventory of printer cartridges. The ink in them can dry out , so they have an expiration date ,which in turn means that store manager does not want to keep too many on hand. On other hand, the manager does not want to be out of stock when a customer wants to buy Cartridges. Assume customer demand occurs one at a time (that is customer never want to buy more than one at a time)according to Poisson process with mean rate of two per week. Assume that the store manager can order replacement stock one carton at a time, where a carton contains six cartridge. . After placing an order for replacement the store has to wait for a period of time(order processing plus delivery)this is negatively distributed with mean of one week. Such an order will be placed by manager as soon as stock falls to one cartridge. 

a) Set up an ergodic markov process model to track level of inventory . The states correspond to no of cartridges in stock .Each customer demand decreases the stock unit by 1 .And replacement will increase it by 6. 

b)what is the probability that customer waiting one these cartridges finds the store out of stock