A Mexican food restaurant, is very popular during lunch time. The manager wants to perform a study on the service level of the restaurant. He hired...

A Mexican food restaurant, is very popular during lunch time. The

manager wants to perform a study on the service level of the restaurant. He hired an

operations analyst to take this study. The findings are as follows. The counter of the

restaurant can process only one customer at a time. During lunch time, approximately

there are 10 customers in every 20 minutes (assuming this is a Poisson stream). It takes

on average 3 minutes for the counter to help one customer (assuming the service time

follows exponential distribution). The waiting line cannot exceed 25 people.

a. What is the probability the counter can relax during lunch time?

b. What is average amount of people waiting in the line?

c. What is the expected total duration for a customer to purchase the food?

d. What if the restaurant open another counter? Please recalculate (a), (b), and (c).