Reference no: EM132295499

The National Overnight (NatO) company has a new competitor based in Kansas City that is taking away some of their business. Airplanes still arrive 24 hours a day at the national hub in Dallas but the frequency of arrivals is declining due to the new competition. The contents of the planes are still unloaded onto cargo vans each capable of holding 1,000 packages. The cargo vans transport the packages to the sorting center. The sorting center has a large storage area designed to hold up to 49,000 packages. After being sorted, another fleet of cargo vans transports the packages to the outgoing planes. However, the following information details the receiving process only. During the night (6 p.m. to 6 a.m.), airplanes arrive at a high rate providing a continuous arrival flow of packages with an average rate of 24,000 packages per hour. However, during the day (6 a.m. to 6 p.m.) air landings are less frequent, resulting in an average arrival rate of 5,000 packages per hour. NatO has also decided to reallocate their employees across three shifts instead of two shifts. Two night shifts (6 p.m. to 2 a.m. and 2 a.m. to 10 a.m.) processing 21,000 packages per hour and one day shift (10 a.m. to 6 p.m.) processing 9,000 packages per hour. Even with this new work arrangement, cargo vans are still expected to wait to unload at the sorting center during some portions of the night shift - though the hope is that the van lines will be shorter. Cargo van drivers are paid $10/hour, benefits included. NatO begins each night with completely empty storage bins at 6 p.m. Cargo vans begin waiting as soon as the storage area is full. What is the maximum number of cargo vans waiting in line at any given during a 24-hour period? Input your answer as a whole integer such as "17" or "9". If capacity is such that no vans ever have to wait then input "0".