Continuous Flow $-$ One$-$at$-$a$-$time with Setup and Batching: Consider a single$-$machine station fabricating a part as follows: The station produces parts one$-$at$-$a$-$time in batches of Q units, where Q is specified $($known$).$ Every time a batch of Q units of the product is produced, there is a fixed setup time S and a batch processing time of Q x t$,$ where t $=$ unit process time for one part.$$

Write an expression for the maximum throughput, TH $=$ rb$,$ and minimum average cycle time, CT $=$ T$0,$ for this single$-$machine, single$-$station line. What would be the critical WIP W$0$ for this line? Your answers should be in terms of parameters S$,$ Q$,$ and t$.$

Suppose S $=2$ hours, Q $=10,$ t $=1$ hour, calculate the value of the critical WIP W$0$ for this line.