Consider a process that consists of three steps $1,2$ and $3.$ Steps $1$ and $2$ are each equipped by a single machine. Step $3$ is performed by a single worker. Each of the process steps works on one unit of work at a time, but must complete a $$set up$$ between production batches. The required processing times and set$-$up times at each of the steps are listed below. There is unlimited space for buffer inventory between these steps. The system has an unlimited supply of work available to be performed $($i$.$e$.,$ demand exceeds capacity$).$

Process step Set up time Activity time

$150$ min $2$ min$/$unit

$2120$ min $1$ min$/$unit

$305$ min$/$

Assume that the process starts empty, that set$-$ups at steps B and C can not begin until work arrives, that the production batch is $10$ units at each step, and the transfer batch between steps $1$ and $2,$ and between steps $2$ and $3$ is $1$ unit $($i$.$e$.,$ the unit completed at one step may be passed immediately to the next step$).$ How long does it take to complete a batch of $10$ units?

Assume that the process starts empty, that set$-$ups at steps B and C can not begin until work arrives, that the production batch is $10$ units at each step, and the transfer batch between steps $1$ and $2,$ and between steps $2$ and $3$ is $1$ unit $($i$.$e$.,$ the unit completed at one step may be passed immediately to the next step$).$ How long does it take to complete a batch of $10$ units?

$125$ minutes

$134$ minutes

$187$ minutes

$190$ minutes

None of the above