Jessica Mendoza owns a small ice cream shop, The Cherry Ice Cream Republic, in the Traverse City area (Michigan). She primarily serves tourists who visit the area during the summer, when the demand can fluctuate widely depending on the time of the day, the day of the week, or, in some cases, whether there is a festival going on (the biggest one in the area is the Cherry Festival that takes place just after the 4^th of July). A major concern for Jessica is the customers waiting time and the space that she has available for customers to wait. One thing that Jessica has learned is that if the customers have to wait too long or if there is not enough space in the waiting line, they will leave.

She has collected some past data to study this problem. She knows that on average she gets about 31 customers per hour. Each customer spends about 10 minutes in the storethis time consists of placing the order, waiting for the ice cream, paying, waiting for the change, if any, and then leaving. His shop can accommodate about 8 customers waiting in line. Jessica also knows that the demand can swing widely. For example, last year, during the Cherry Festival, she had over 51 customers per hour at the peak (11 a.m. to 3 p.m.). She remembered that because she found herself pitching in to help with filling the orders. Jessica also knows that the demand can be as low as 6 customers per hour (again, last year over a three-day period of low temperatures in July).

a. On average, does Jessicas shop have enough space for her customers to wait? (Hint: Use Littles law.)

b-1. Would Jessica be satisfied with the average space available in her shop?

b-2. Is it good enough to just look at the averages?

c. What recommendations would you offer Jessica? (Hint: Think about how low the service time would have to be to accommodate a customer demand of 51 per hour.)