The following table lists the required processing times and setup times at each of the steps. Assume that the unit of production is a wafer, from which individual chips are cut at a later stage.

Note: A setup can only begin once the batch has arrived at the machine.

Process Step $1$ Depositing $2$ Patterning $3$ Etching

Setup time $47$ min. $33$ min. $23$ min.

Processing time $0\mathrm{.}17$ min.$/$unit $0\mathrm{.}27$ min.$/$unit $0\mathrm{.}22$ min.$/$unit

$($a$)$ What is the process capacity in units per hour with a batch size of $100$ wafers? $($Round your final answer to the nearest whole number.$)$