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

Step $1$ Step $2$ Step $3$

Processing Time $0\mathrm{.}3$ min$/$part $0\mathrm{.}4$ min$/$part $0\mathrm{.}35$ min$/$part

Setup Time $60$ min. $45$ min. $45$ min.

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? $($Round the answer to $2$ decimal places.$)$