In a workcenter, Machine A has a $10-$minute set$-$up time per batch and a $2-$minute per unit run time. Machine B performs the identical function but has a set$-$up time of $30$ minutes and a $1-$minute run time per unit. The work center makes products in batches ranging from $1$ unit to $100$ units. Assuming capacity is not a limitation on either Machine, in order to minimize the total processing time, on which batches should Machine B be used?

Batches of more than $20$ units should be run on Machine B$.$

All batches should be run on Machine B$.$

Batches of fewer than $80$ units should be run on Machine B$.$

Batches with up to $50$ units should be run on Machine B$.$

No batches should be run on Machine B