An operator attends five automatic machines. After each machine completes a batch run, the operator must reset it before a new batch is started. The time to complete a batch run is exponential with mean 45 minutes. The setup time is also exponential with mean 8 minutes.

(a) Determine the average number of machines that are awaiting setup or are being set up.

(b) Compute the probability that all machines are working.

(c) Determine the average time a machine is down.