The figure below details the process flow for two types of customers who enter Barbara's Boutique shop for customized dress alterations. After step T$1,$ Type A customers proceed to step T$2$ and then to any of the three workstations at T$3,$ followed by steps T$4$ and T$7.$ After step T$1,$ Type B customers proceed to Step T$5$ and then steps T$6$ and T$7.$ The numbers in parentheses are the minutes it takes to process a customer.

a$.$ What is the capacity of Barbara's shop in terms of the numbers of Type A customers who can be served in an hour? Assume no customers are waiting at steps T$1$ or T$7.3$ customers. $($Enter your response rounded down to the next whole number.$)$

b$.$ If $30$ percent of the customers are Type A customers and $70$ percent are Type B customers, what is the average capacity of Barbara's shop in customers per hour? customers. $($Enter your response rounded to two decimal places.$)$

c$.$ Assuming that the arrival rate is greater than five customers per hour, when would you expect Type A customers to experience waiting lines, assuming no Type B customers in the shop?