A furniture factory makes two types of wooden tables, large and small.

Setup

Time,

Minutes Run

Time per

Piece,

Minutes Capacity,

Pieces

per Hour

Wood cutting $30515$

Make four legs $601010$

Make tops $60128$

Finish the wood $20812$

Assemble and ship $201714$

Small tables are made in batches of $100,$ and large tables are made in batches of $50.$ A batch includes a fixed setup time for the entire batch at each process step and a run time for each piece in the batch. Both large and small tables have the same processing times. The capacities of each process step are given, and apply to production of either type of table, as shown in the flowchart.

a$.$ What is the capacity of the system, and what is the bottleneck?