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Inventory Build - up and Little's Law ( 1 7 points ) . Falafel Pro is a popular takeout restaurant, offering falafel sandwiches to customers

Inventory Build-up and Little's Law (17 points).
Falafel Pro is a popular takeout restaurant, offering falafel sandwiches to customers weekday lunch time (between 11AM and 2PM). Because of its popularity, customers start to line up from 10:45AM, although Falafel Pro opens at 11 AM. Customers show up at a rate of 40 per hour from 10:45-11AM, at a rate of 80 per hour from 11-11:30AM, at a rate of 200 per hour from 11:30-1:00PM, and finally, at a rate of 120 per hour from 1-2:00PM. The restaurant closes at 2:00PM regardless of the number of customers waiting in line, and the unsatisfied customers are sent away. Suppose that every customer who shows up willingly joins the line and waits until satisfied or sent away. Falafel Pro starts serving customers at 11AM at the rate of 180 customers per hour.
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