She has collected some data from the past to study this problem. She knows that on average she gets $43$ 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 $63$ 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$)?$