9. consider Example below, where the states are The probability of each possible transition from the state in one week to the state in the following week stays the same as in the lecture example. But the maintenance policy is different, which will change the transition matrix. If the machine is in state 0 or 1 , do nothing, therefore, there is an expected cost of $1000 due to defective items in state 1 , and there are no defective items if machine in state 0 . If the machine is in state 2 or 3 , the machine will be replaced, therefore, there is a lost profit of $2000 and a replacement cost of $4000. (a) What is the transition matrix P ? (b) Use the method in Sec. 29.5 to calculate the steady-state probabilities. (c) What is the long-run expected average cost per week