A newly constructed cafeteria at a large government office expects to service 80

Question

A newly constructed cafeteria at a large government office expects to service 800 people per day. Since most workers begin their lunch break between 12:00pm and 12:40pm, food and cashier stations must be able to process a large number of workers over a short period of time.

a) Assume that the 800 workers arrive to lunch at a uniform rate between 12:00pm and 12:40pm. If it takes 15 seconds for a cashier to process a customer, how many cashiers are needed to avoid a line?

b) Each standard cash register costs $2,000. A deluxe cash register equipped with an automatic change-issuing machine, sells for $2,500. The automatic change-issuing machine is thought to reduce processing time per customer from 15 to 12 seconds. Which type of cash register do you recommend buying?

Explanation / Answer

A) if 800 workers arrive to lunch at uniform rate between 12:00 to 12:40 pm, this mean total time would be 40 mins,

if single cashier take 15 seconds on single customer then, single cashier can take 160 customer in 40 mins, for avoiding the line we would be needing 5 cahsier 160*5 = 800 to cover all wokers in 40 min by avoiding the line.

60/15= 4, 4 customer would be cover in 1 min by single cashier,

single cashier can cover 40*4= 160 workersin 40 mins,

800/160= 5 cashier would be need to avoid line.

B) I would recommemd automatic change- issuing machine, because it would be saving lot of time with $500 more only in camparision to standard cash register, it can help in saving the extra cashier cost also, no queing would be their.

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