A small computer store has room to display up to three computers for sale.

Customers come at times of a Poisson process with rate 2 per week to buy a computer and will buy one if at least one is available. When the store has only one computer left it places an order for two more computers. The order takes an exponentially distributed amount of time with mean 1 week to arrive. Of course, while the store is waiting for delivery, sales may reduce the inventory to 1 and then to 0. (a)Write down the matrix of transition rates Qij and solve Q D 0 to find the stationary distribution.

(b) At what rate does the store make sales?