The$$ three$-$station work cell at Pullman$$ Mfg$.,$ Inc. is illustrated in the figure below. It has two machines at station $1$ in parallel$($i$.$e$.,$ the product needs to go through only one of the two machines before proceeding to station$2).$

Station $1$

Machine A

Station $1$

Machine B

Station $2$

Station $3$

$30$ min$/$unit

$30$ min$/$unit

$4$ min$/$unit

$12$ min$/$unit

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 $1$ take $30$ minutes per unit. Station $2$ takes $4$ minutes per unit. Station $3$ takes $12$ minutes per unit.

Part $2$

$$a$)$ The throughput time is

$$

$46$ minutes $($enter your response as a whole$$ number$).$

Part $3$

$$b$)$ The bottleneck time of this work cell is

$$

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

BY THE WAY THE ANSWER IS NOT $20$ OR $30$