Problem $2$: Sandwich Restaurant $(40$ points$)$

Consider the sandwich restaurant Which Wich. The process goes as follows:

A customer enters the restaurant and grabs the sandwich bag corresponding to the type of sandwich she wants $($chicken$,$ seafood, vegetarian, etc.$).$ She fills out the list of ingredients she wants $($marked on the bag$)$ and gives the sandwich bag to Adam $($who works at the cash register$).$ It takes a customer exactly $90$ seconds to finish all the above steps after she$/$he arrives to the restaurant.

Adam checks into the order and asks the customer what drink she$/$he wants, which takes $15$ seconds; accepts the customer's payment, which takes $1$ minute; and fills up the drink at the soda fountain for the customer, which takes $30$ seconds. Then Adam puts the sandwich bag on the "order rack" above the counter, which takes $15$ seconds.

The order on the sandwich bag is then read by Bob who picks the bread, adds the cheese and the meat and put the sandwich into a toaster oven. Altogether it takes Bob $90$ seconds to finish this step.

The sandwich stays in the oven for exactly $2$ minutes. The oven is small and can hold only one sandwich at a time.

Once the sandwich comes out of the oven, Bob $($the same Bob as in the above$)$ adds the rest of the ingredients to it $($mayonnaise$,$ vegetables, spices, etc.$)$ according to the order on the sandwich bag; then he takes the sandwich bag off the order rack, puts the sandwich in the bag and takes it to the customer. In total, it takes Bob $1$ minute to finish this step.

When the sandwich is ready, the customer picks it up and leaves immediately.

Further, we make the following assumptions:

The steps and times listed above are the same for all the types of sandwiches that can be ordered and for all customers;

Every customer orders a sandwich and a drink;

There is an infinite amount of ingredients for the sandwiches so that the workers never run out of ingredients;

There is infinite space in the restaurant to put the bags above the counter or let customers wait;

There are infinite pens for the customers to fill out the order

Answer the following questions $($please provide the steps$)$:

$($a$)$ Draw a process flow diagram for this process. $(15$ points$)$

$($b$)$ What is the process capacity and where is the bottleneck? $(15$ points$)$

$($c$)$ What is the rush order flow time? $(10$ points$)$