Answer the following questions showing work based on the given assumptions: Stage A

$$ Can produce $20$ cars$/$hour

$$ Initial set up time is $20$ minutes when changing the car model or size

Stage B

$$ Can produce $20$ cars$/$hour

$$ Must be shut down for maintenance and cleaning for $30$ minutes after every $90$ minutes of operation

Stage C

$$ Can produce $18$ cars$/$hour

$$ This stage takes longer due to customization but there is no setup or downtime

now consider this:Part B $$ Multi$-$model Scenario $($use the base model on this from Part A without buffers and$/$or setup time reduction$)$

Now consider that you are working with $3$ different car models, model x$,$ model y$,$ and model z and that set up is only required when you are changing the model type in stage A$.$ Also consider $8-$hour shift per day and $6-$day per week operation.

$1)$ What would be the batch sequence with $3$ models?

$$ Come up with a batch sequence across the $6$ days of the week minding the rules laid out:

i$.$ Each model must have at least one batch each day

ii$.$ Equal number of batches need to be sequenced by the end of the week

$2)$ How many of each models can I produce?

$3)$ Repeat the above with $4$ models