Quick Lube Inc. operates a fast lube and oil change garage. On a typical day, customers arrive at the rate of three per hour, and lube jobs are performed at an average rate of one every 15 minutes. The mechanics operate as a team on one car at a time.

Assuming Poisson arrivals and exponential service, find

a. Utilization of the lube team.

b. The average number of cars in line.

c. The average time a car waits before it is lubed.

d. The total time it takes to go through the system (that is, waiting in line plus lube time).