I. The Burger Bistro $(50$ points$)$

You stop by your old hang out, The Burger Bistro. Mr$.$ Davidson has heard from your parents that you$$re a star student in one of those big time business schools and he asks you to help him out. It seems a problem has emerged because of the delay in delivery of his famous sandwich, the $$Double Decker$.$ Mr$.$ Davidson states he$$s experiencing pressure to decrease burger preparation time in order to meet increasing demand.

The sequential process steps start with Delane cooking the beef patties. The grill can cook $6$ beef patties at the same time. Beef patties take $1\mathrm{.}5$ minutes to cook and $1\mathrm{.}5$ minute to cool down $($additional patties can$$t be started until cooling is complete$).$ Delane places the cooked patties on the shelf for easy access to assembly. Note: two patties are required for each $$Double Decker$$ burger.

Assembly of the $$Double Decker$$ starts with Priyanka who takes the bottom bun, places a beef patty, salt and cheese on top of it and gives it to Alex in $20$ seconds.

Alex places lettuce, sauce and onions on the burger in $15$ seconds and passes it to Cole.

Cole puts the middle bun and second beef patty, salt and cheese on; this takes another $20$ seconds.

Sean then adds lettuce, sauce, pickles for the second layer and then adds the sesame seed top bun. Sean$$s step takes $12$ seconds and he passes the burger to Brian.

Brian wraps the burger and places it in the chute in $6$ seconds to be served to customers.

Process steps can not start until the previous step has been completed.

a$.(25$ points$)$ What is the capacity of each step in the process in number of completed $$Double Decker$$ burgers prepared per minute $($Delane$,$ Priyanka, Alex, Cole, Sean, Brian$)?$ What step $/$ who is the bottleneck? What is the system capacity in completed $$Double Decker$$ burgers $/$ minute?

Process Step Capacity

Double Decker burgers $/$minute

Delane

Priyanka

Alex

Cole

Sean

Brian

System

Bottleneck: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$