Calculate the average profit, Basic Statistics

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.

 

Posted Date: 3/26/2013 8:01:27 AM | Location : United States







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