$($Setup Everywhere$)$ 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 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.$)$

a$.$ What is the capacity of step $1$ if the batch size is $35$ parts?

b$.$ For what batch sizes is step $1$ the bottleneck?

c$.$ For what batch sizes is step $2$ the bottleneck?

d$.$ For what batch sizes is step $3$ the bottleneck?