Question

MP Nails Salon is run by two nail artists, Makayla Mani and Penny Pedi, each capable of serving 6 customers per hour, on average. Eight customers, on average, arrive at the salon each hour.

If all arriving customers wait in a common line for the next available stylist, how long would a customer wait in line, on average, before being served?

Answer 1

The MP Nails Salon can serve 12 customers per hour with two nail artists and receives an average of eight customers per hour. The service rate exceeds the arrival rate; therefore, the average waiting time for customers is expected to be negligible.

Step-by-step explanation:

The question revolves around the average wait time for customers at the MP Nails Salon, which has two nail artists, Makayla Mani and Penny Pedi, and receives an average of eight customers per hour. Each nail artist is capable of serving six customers per hour, making the total service capacity 12 customers per hour. With an average arrival rate of one customer every two minutes, or 30 customers per hour, there is a surplus in service capacity. However, the provided information suggests eight arrivals per hour, meaning the average arrival rate is actually one customer every 7.5 minutes.

Since the service rate is higher than the arrival rate (12 customers served per hour vs. 8 customers arriving per hour), a queue is unlikely to form. Thus, the average waiting time for each customer before being served would be minimal, possibly even zero.