Jessica Mendoza owns a small ice cream shop, The Cherry 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 time of day, 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 customer$$s waiting time and the space that she has available for customers to wait. One thing that Jessica has learned is that if the customers must wait too long or if there is not enough space in the waiting line, they will leave.

She has collected some data from the past to study this problem. She knows that on average she gets $38$ customers per hour. Each customer spends about $9$ minutes in the store $$ this time consists of placing the order, waiting for the ice cream, paying, waiting for the change, if any, and then leaving. Her shop can accommodate $8$ customers maximum. Jessica also knows that the demand can swing widely. For example, last year, during the Cherry Festival, she had $58$ customers per hour at the peak $(11$am to $3$pm$).$ She recalls pitching in to help to fill the orders during that time.

a$.$ At the average demand rate, does Jessica$$s shop have enough space for her customers? $($Hint: Use Little$$s law to compute the average number of customers in the store at the average demand rate$).$

b$.$ At peak demand rate, does Jessica$$s shop have enough space for her customers? $($Hint: Use Little$$s law to compute the average number of customers in the store at the peak demand rate$).$

c$.$ At what demand rate would Jessica just barely have sufficient space for her customers $($on average$)?$