Q$5\mathrm{.}3($Algo$)$ Simple Set$-$Up $[5\mathrm{.}1,5\mathrm{.}6]$

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

Work is processed in batches at each step. Before a batch is processed at step $1,$ the machine has to be set up$.$ During a setup, the machine is unable to process any product.

$($a$)$ Assume that the batch size is $52$ parts. What is the capacity of the process?

The process capacity of the entire process is units$/$hr

$($b$)$ For a batch size of $10$ parts, which step is the bottleneck for the process? c$)$ What batch size would you choose?

Batch size is

units

d$)$ Suppose the batch size is $36$ parts. What would be the average inventory after step $1?$ Assume step $1$ can use idle time so its production rate does not exceed the capacity of the process.