Consider the following batch$-$flow process consisting of three process steps performed by three machines:Step $1$ Step $2$ Step $3$Activity Time: Activity Time: Activity Time:$0\mathrm{.}25$ Minute$/$Part $0\mathrm{.}20$ Minute$/$Part $0\mathrm{.}15$ Minute$/$PartSetup Time: Setup Time: Setup Time:$30$ Minutes $20$ Minutes $45$ MinutesWork 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 $1(2,3)$ the bottleneck?