Consider the following batch$-$flow process consisting of three process steps performed by three machines: Step $1->$ Step $2->$ Step $3->$ Process Time $0\mathrm{.}20$ min$/$unit $0\mathrm{.}40$ min$/$unit $0\mathrm{.}25$ min$/$unit Setup Time $30$ mins $20$ mins $35$ mins Suppose units are produced in batches of $50,$ what is the capacity of Step $2($in units$/$min$)?$ The goal of the problem is to advice the process on what batch size to choose.

Before a batch is processed at Step $1,$ Machine $1$ has to be set up for $40$ minutes. During setup,

the machine is unable to process any product. The demand of the process is $12$ units per hour