A manufacturing company produces $500$ units of a product per day using two processes, A and B$.$ Process A has a cycle time of $30$ minutes per unit, while process B has a cycle time of $20$ minutes per unit. If both processes operate for $8$ hours per day, calculate:

a$)$ The total daily production capacity of each process.

b$)$ Identify the bottleneck process.

c$)$ Determine the maximum number of units the company can produce per day.