Car wash offers two types of washes: Standard and Deluxe. The process flow for both types of customers is shown in the following chart. Both wash types are first processed through steps Al and A$2.$ The standard wash then goes through steps A$3$ and A$4$ while the deluxe is processed through steps A$5,$ A$6,$ and A$7.$ Both offerings finish at the drying station A$8.$ The number in the parenthesis indicates the minutes it takes for that activity to process a customer.

a$)$ Which step is the bottleneck for the standard car wash process? For the deluxe car wash process?

b$)$ What is the capacity $($measured as customers served per hour$)$ of car wash to process standard and deluxe customers?

c$)$ If $60$ percent of the customers are standard and $40$ percent are deluxe, what is the average capacity of the car wash in customers per hour?