Consider a bagel store selling three types of bagels that are produced according to the process flow diagram outline below. We assume the demand is $180$ bagels a day, of which there are $30$ 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.

Moreover, we assume the following Processing times:

Cut Grilled Stuff Veggies Cream Cheese Wrap

Processing Time $3[$min$/$bagel$]10[$min$/$bagel$]5$

$[$min$/$bagel$]4$

$[$min$/$bagel$]2$

$[$min$/$bagel$]$

Processing 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 on hour, assuming the product mix has to remain constant?