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A machine is used for machining of a manufactured product. At the beginning of each business day inspection reveals the machine's condition. There are three possible states: 0, 1 and 2. In state 0, the machine is unproductive and must be repaired. The repair costs $ 500 per day and can last more than a day. When the repair is completed, the machine is in perfect working condition (condition 2) and can operate at full capacity, which refers income of $ 400 per day. When the machine is in state 1, it can be used only at half speed, which yields $ 200 per day. In these conditions, assumes that the machine state changes according to a Markov chain with the probability following transition:
0.2 0 0.8
0.4 0.6 0
0.1 0.2 0.7
(A) On average, how many consecutive days the machine is in state 0 ?
(B) On average, what percentage of days the machine is productive?
(C) Calculate the average profit per day.
a few problems
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