Statement of a problem № m1379


Ye Olde Creamery, a popular ice cream store on campus, has one line for its tasty treats. Students arrive at the Creamery about one every minute. Because of the new automated “Wave N Pay” payment system, it only takes about 40 seconds, on the average, to place and then pay for an order as students need only hold their cell phones over the “Wave N Pay” device and the system automatically deducts the cost of the ice cream cone from their account. However, the “Wave N Pay” system is finicky and is often offline, causing students to pay with cash. This causes the average order and pay times to double and a long line to form, forcing Ye Olde Creamery to open another order and pay station. Having two order and pay stations open (with just one line) costs the Creamery an extra $12.00 an hour while upgrading the “Wave N Pay” system to never go offline would cost $1200. Assuming Poisson arrivals and negative exponential service times compare the operation of Ye Olde Creamery with the two different configurations. Given the additional costs involved, what should the management of Ye Olde Creamery do?


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