The National Overnight (NatO) company provides express smallpackage delivery overnight. Airplanes arrive 24 hours a day at thenational hub in Dallas where their contents are unloaded onto cargovans each capable of holding 1,000 packages. The cargo vanstransport the packages to the sorting center. The sorting centerhas a large storage area designed to hold up to 50,000 packages.After being sorted, another fleet of cargo vans transports thepackages to the outgoing planes. However, the following informationdetails the receiving process only. During the night (6 p.m. to 6a.m.), airplanes arrive at a high rate providing a continuousarrival flow of packages with an average rate of 25,000 packagesper hour. However, during the day (6 a.m. to 6 p.m.) air landingsare less frequent, resulting in an average arrival rate of 5,000packages per hour. NatO runs two 12-hour shifts at the sortingcenter: the night shift starts at 8 p.m. and leaves by 8 a.m. Thenight shift has the largest number of employees and can process upto 21,000 packages per hour. The day shift, on the other hand, issmaller and can process up to 12,000 packages per hour from 8 a.m.to 8 p.m. It is known that the cargo vans typically had to wait tounload at the sorting center during some portions of the nightshift. Cargo van drivers were 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. Whatis the maximum number of cargo vans waiting in line at any givenduring a 24-hour period? Input your answer as a whole integer suchas "17" or "9". If capacity is such that no vans ever have to waitthen input "0".
