Consider a bagel store selling three types of bagels that are produced according to the process flow diagram outlined below. We assume the demand is $180$ bagels a day, of which $30$ grilled veggie, $110$ veggie only, and $40$ cream cheese. Assume that the workday is $10$ hours long and each resource is staffed with one worker. The activity times are given in the flow chart below. Activity times are independent of which bagel type is processed at a resource $($for example, cutting a bagel takes the same time for a cream cheese bagel as for a veggie bagel$).$

a$.$Where in the process is the bottleneck?

b$.$ How many units can the process produce within one hour?

b$.$ The bakery begins batches every $11/2$ hours on both lines.