3. (35 points) A building has two elevators (E1 and E2), where each one can be working or damaged. If E1 is working today, the probability of working tomorrow is 1/2, otherwise, it will need repairing. Likewise, if E2 is working today, the probability of working tomorrow is 2/3, otherwise, it will need repairing. The building only counts with one repairman. Therefore, if both elevators are not working, the repairman will always work in E1 rst. If an elevator is being xed on a particular day, the next day is working with probability is 1. Assume that the repairman spends all day repairing the elevator. The building manager knows that if the E1 is not working, it will cost $1000 per day, while E2 will cost only $500 per day. (a) (20 points) Dene the Markov Chain model by clearly dening the states and the transition probability matrix. You do not need to draw the state transition diagram for credit. (b) (10 points) Estimate the expected number of elevators working in steadystate. (c) (5 points) In the long run, estimate the expected total costs of the elevators not working on any given day