Problem $3-19($Algo$)$

Jessica Mendoza owns a small Ice cream shop, The Cherry Cream Republic, in the Thaverse City ared $($Michigan$).$ She primarlly serves tourists who visit the area during the summer, when the demand can fluctuate whdely 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 concem for Jessica is the customer's walting time and the space that she has avallable for customers to walt. Ohe thing that Jessica has learned is that if the customers must walt too long or if there is not enough space in the walting line, they will leave.

She has collected some data from the past to study this problem. She knows that on average she gets $26$ customers per hour. Each customer spends about $12$ minutes in the store $-$ this time consists of plaching the order, walting for the ice cream, paying. walting 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 exampla last year, during the Cherry Festlval, she had $45$ customers per hour at the peak $(11$am to Spm$).$ She recalis pltching 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 ratel

b$.$ At peak demand rate, does Jesslca's shop have enough space for her customers? $($Hint Uee Littles 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 averagel?

Required A Required B Required $C$

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

Note: Do not round intermediate calculations. Enter your first answer to $2$ decimal places.

$\backslash$table$[[$Average number of customers in store$],[$Is sufficient space available, on average?$]]$