# Question & Answer: At a make-to-order hamburger shop, there is one worker who grills patties, two workers who assemble…..

At a make-to-order hamburger shop, there is one worker who grills patties, two workers who assemble burgers, and one cashier. Their grill can grill patties in 4 minutes and the grill can cook up to 20 patties at one time. Each burger assembler can assemble a burger in 40 seconds. It takes the cashier 6 seconds to collect payment. What is the capacity of the hamburger restaurant in customers per minute? What is the bottleneck? Assume on burger per customer. If two more burger assemblers are hired, what is the capacity of the burger store? What is the bottleneck? Disregarding part b, if the restaurant buys another grill, what is the capacity of the restaurant? What is the bottleneck? (Assume the one griller can use both grills.)

a) Grill can cook 20 patties in 4 minute

Time to assemble each burger = 40 seconds

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Time taken by cashier = 6 seconds

Total time taken by one burger = 4 minute + 40 seconds + 6 seconds

Time taken to serve 20 burgers = 240 seconds + 400 seconds (20 burger and 2 worker) + 120 seconds (20 burger)

= 760 seconds

In this case, second round of burger preparation cannot be started because 480 seconds (second reound ) + 40 seconds is less than last burger preparation in first round.

thus capacity of hamburger restaurant= 20 * 60/760

=1.5 customer/minute i.e 1 customer/minute

Bottleneck is burger assemblers

b)

Time taken to serve 20 burgers = 240 seconds + 200seconds (20 burger and 2 worker) + 120 seconds (20 burger)

= 560 seconds

thus capacity of hamburger restaurant= 20 * 60/560

= 2 customer/minute

Bottleneck= Grill

c)

Time taken to serve 40 burgers = 240 seconds + 800 seconds (20 burger and 2 worker) + 240 seconds (20 burger)

= 1280 seconds

thus capacity of hamburger restaurant= 40 * 60/1280

= 1.875 customer/minute i.e 1 customer/minute

Bottle neck= burger assemblers