$.$ The following diagram represents a manufacturing process, which consists of five production stages, A$,$ B$,$ C$,$ D$,$ and E$.$ Setup times and run times are given in Table $1.$

TABLE $1$

STAGE SETUP TIME PER LOT

$($minutes$)$ PROCESSING TIME PER UNIT $($minutes$)$

A $303$

B $451$

C $202$

D $205$

E $102$

Assume that after processing each lot a new setup is required and all setups are done when a lot arrives to a stage and the company has determined that lot size will be $20$ units.

a$.$ Identify the bottleneck stage

b$.$ What is the cycle time?

c$.$ What is the throughput time?

d$.$ What is the work$-$in$-$process inventory?

e$.$ Assume the company is operating three shifts of $8$ hours. What is the daily capacity of the operation $($at steady state$)?$

f$.$ How much idle time does each stage have?

g$.$ What will be the throughput time and work$-$in$-$process inventory if idle time at stages are used for setup?