$2$a$.$ Step $3$ is the bottleneck with the longest processing time $=10$ minutes$/$unit $=6$ units$/$hour Without an inventory buffer, what is the average capacity of the bottleneck in units$/$hour$?($Hint capacity is in units$/$time$.$ Calculate how many units can be produced by Step $3$ in $1$ hour and $15$ minutes $(1\mathrm{.}25$ hours$)?$ Keep in mind that, during $15$ minutes $(0\mathrm{.}25$ hours$),$ Step $3$ cannot produce anything because Step $2$ is being maintained.$)$

$2$b$.$ If you can have one inventory buffer in this system to keep the bottleneck $($Step $3)$ working even when Step $2$ is being maintained for $15$ minutes, where would you put it$?$ Explain your answer.

a$)$ between Step $1$ and Step $2$

b$)$ between Step $2$ and Step $3$

c$)$ between Step $3$ and Step $4$