Question:

A manufacturing company produces widgets using two processes: Process A and Process B$.$ Process A has a daily capacity of $500$ units, while Process B has a daily capacity of $700$ units. The company operates $8$ hours per day. If Process A takes $30$ minutes to produce one unit, and Process B takes $20$ minutes per unit, determine:

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

b$)$ Which process is the bottleneck.

c$)$ The maximum number of units produced per day.