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 $41$ parts. What is the capacity of the process?

The process capacity of the entire process

is

$($b$)$ For a batch size of $5$ parts, which step is the bottleneck for the process?

$($c$)$ What batch size would you choose?

$($d$)$ Suppose the batch size is $32$ 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.

Help with part c and d