Reconsider Problem 1. Now suppose that the manufacturer keeps a spare machine that only is used when the primary machine is being repaired. During a repair day, the spare machine has a probability of 0.15 of breaking down, in which case it is repaired the next day. Denote the state of the system by (x, y), where x and y, respectively, take on the values 1 or 0 depending upon whether the primary machine (x) and the spare machine (y) are operational (value of 1) or not operational (value of 0) at the end of the day. (a) Construct the (one-step) transition matrix for this Markov chain (b) If it costs $1150 to repair the primary machine and $250 to repair the spare machine, what is the expected daily cost of operation? (c) Compute the expected number of days needed for the system to go from state when only the spare machine is operational to the state when only primary machine is op- erational (d) Compute the expected time before the system returns to the state with only spare machine operational Reconsider Problem 1. Now suppose that the manufacturer keeps a spare machine that only is used when the primary machine is being repaired. During a repair day, the spare machine has a probability of 0.15 of breaking down, in which case it is repaired the next day. Denote the state of the system by (x, y), where x and y, respectively, take on the values 1 or 0 depending upon whether the primary machine (x) and the spare machine (y) are operational (value of 1) or not operational (value of 0) at the end of the day. (a) Construct the (one-step) transition matrix for this Markov chain (b) If it costs $1150 to repair the primary machine and $250 to repair the spare machine, what is the expected daily cost of operation? (c) Compute the expected number of days needed for the system to go from state when only the spare machine is operational to the state when only primary machine is op- erational (d) Compute the expected time before the system returns to the state with only spare machine operational