At the local movie theater (e.g., AMC), the number of moviegoers arriving at the ticket counter is assumed to be Poisson at 2 people per minute. A single attendant at the ticket counter performs each ticket sale at an average rate of 40 seconds (exponentially distributed).

a. Will this system reach steady-state? A second attendant opens up another window at the ticket counter.

Calculate the following:

b. What is the probability that both attendants are idle?

c. What is the expected number of moviegoers waiting in line?

d. What is the expected waiting time to reach the ticket counter?

e. If the cost to open one window is $25 per hour and the customer’s waiting time is worth $15 per customer-hour, then how many attendants should be working to minimize the expected hourly costs?