A hub is a central airport that flights are routed through, and spokes are the routes that planes take out of the hub airport. A good example of a hub-and-spoke system is that of Delta Airlines, which has its hub at Hartsfield Atlanta internotional Airport. Let's say you are in Charleston, SC, and want to go to Memphis, TN. There's probably not a lot of demand for a Charleston-to-Memphis flight, so the airline flies you from Charleston to Atlanta, and then from Atlanta to Memphis via a connecting flight. Most major airlines have multiple hubs. They claim that hubs allow them to offer more flights for passengers. Most of the 12 major U.S. passenger airlines in operation as of 2001 use a hub-andspoke network to route their plane traffic. In the case of BUCKEYE Airlines, each hub is used for connecting flights to and from cities within 1000 miles of the hub. BUCKEYE Airlines runs flights among the following 12 cities: Atlanta, Boston, Chicago, Denver, Houston, Los Angeles, New Orleans, New York, Pittsburgh, Salt Lake City, San Francisco, and Seattle. To answer the following questions, you will first have to write down the mathematical formulation and then set this up as an integer programming problem. 1. The company wants to determine the smallest number of hubs it will need to cover all of these cities, where a city is "covered" if it is within 1000 miles of at least one hub. 2. BUCKEYE Airlines want to keep New Orleans as one of its bases. Now determine the minimum number of hubs required