Q$5\mathrm{.}3($Algo$)$ Simple Set$-$UpConsider the following batch flow process consisting of three process steps performed by three machines:Step IStep $2$Step $3$Processing Time:$1$ Minute$/$PartProeessing Time:$2$ Minutes$/$PartProcessing Time:$1\mathrm{.}5$ Minutes$/$PartSetup Time:$20$ MinutesNo SetupNo SetupWork is processed in batches at each step. Before a batch laprocessed at step $1,$ the machine has to be set up$.$ During a setup, the machine is unable to process any product.$($a$)$ Assume that the batch size is $44$ parts. What is the capacity of the process?The process capacity of the entire process is$30$ units$/$hr$($b$)$ For a batch size of $10$ parts, which step is the bottleneck for the process?Bottleneck is step $1($c$)$ What batch size would you choose?Batch size is $\_\_\_\_$ units$($d$)$ Suppose the batch size is $32$ parts. What would be the average inventory after step $1?$ Assume step $1$ can use idle time so its production rate does not exceed the capacity of the process.Inventory is $\_\_\_\_$ units