The state of a particular continuous time Markov chain is defined as the number of jobs currently at a certain work center, where a maximum of three jobs are allowed. Jobs arrive individually. Whenever fewer than three jobs are present, the time until the next arrival has an exponential distribution with a mean of 

1 2

 day.

Jobs are processed at the work center one at a time and then leave immediately. Processing times have an exponential distribution with a mean of 

1 4

 day.

(a) Construct the rate diagram for this Markov chain.

(b) Write the steady-state equations.

(c) Solve these equations for the steady-state probabilities.