Consider the following batch$-$flow process consisting $of$ three process steps performed $by$ three machines:

Setup time: $110$ min $180$ min $150$ min

Activity $or$ task time: $8mi\frac{n}{u}$nit $3mi\frac{n}{u}$nit $5mi\frac{n}{u}$nit

Work $is$ processed $in$ batches $at$ each step. Before a batch $is$ processed $at$ a step, the machine $at$ that step must $be$ set $up.(During$ a setup, the machine $is$ unable $to$ process any product.$)$ Assume that there $is$ a dedicated setup operator for each machine $(i.e.,$ there $is$ always someone available $to$ perform a setup $at$ each machine$).$ The batch size $is$ the same $at$ each step. $So,$ for example, $at$ Step $1,if$ the batch size $is10$ units, the time $to$ set $up$ and process the entire batch $is190$ minutes. This $is110$ minutes for the setup, plus $(8$ minutes per unit $*10$ units$)=190$ minutes. When this step $is$ completed, the batch moves $to$ step $2,$ where the setup occurs $at$ that step, followed $by$ processing $at3$ minutes per unit.

$If$ the batch size $is40,$ what $is$ the capacity $of$ Step $2?$ Please report your answer $in$ units $\frac{?}{?}$ hour and keep one $or$ two decimals.

$If$ the batch size $is100,$ what $is$ the capacity $of$ each step? Again, please report your answer $in$ units $\frac{?}{?}$ hour and keep one $or$ two decimals. What $is$ the bottleneck? What $is$ the process capacity?

Assume the batch size $is100.If$ the shop were $to$ add a second machine $to$ Step $1,$ what would $be$ the capacity $of$ the process?