During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each.

If 6 clerks are working the desk, what is the average number in line?

What is the minimum number of clerks to keep the time in the system under 5 minutes?

If each clerk costs $30/hour (remember its the post office!) and customer waiting time costs $20/hour, how many clerks are optimal to give the lowest total cost?

If clerk costs are $30/hour and the waiting costs are $20/hour, what is the total cost at 6 clerks?

For 5 clerks, what is the service rate (mu)?