The$$ three$-$station work cell illustrated in the figure below has a product that must go through one of the two machines at station $1($they are$$ parallel$)$ before proceeding to station $2.$

Station $1$

Machine A

Station $1$

Machine B

Station $2$

Station $3$

Capacity: $20$ units$/$hr

Capacity: $20$ units$/$hr

Capacity:

$2$ units$/$hr

Capacity:

$12$ units$/$hr

A three$-$station work cell has a product that must go through one of the two machines at station $1($they are parallel$)$ before proceeding to station $2$ and then on to station $3.$ Both Machine A and Machine B at Station $1$ have a capacity of $20$ units per hour. Station $2$ has a capacity of $2$ units per hour. Station $3$ has a capacity of $12$ units per hour.

Part $2$

$$a$)$ The bottleneck time of the system is

$$

$30$ minutes per unit $($enter your response as a whole$$ number$).$