The Lead Balloon is a popular '80s rock band that broke up in the 1990s but recently got back together to publish a new CD and go on tour. They want to schedule a summer tour that will encompass 16 possible cities in the eastern half of the United States. However, because of family and business commitments, plus the fact they are not so young and energetic as they used to be, the tour will encompass only 12 weeks, from mid-May to mid-August, when their children will be out of school, so that their families can join them on the tour most of the time. The band also wants to limit the number of concerts each week. Following is a list of the possible cities with the weeks that the local arenas in each city will be available (marked with an X) during the tour. Also included is the concert capacity of the arena in each city.
Based on its popularity and fame it is a foregone conclusion that the band will sell out everywhere it goes.
Thus, the band wants to schedule the cities that will maximize the total attendance at its concerts, which basically means it wants to schedule the cities with the largest arenas, if possible. The band has also stipulated that it wants to perform at least one concert but no more than two concerts each week. Also, because of the band's high-tech equipment and gear, and sound and stage setup requirements, logistical constraints limit the travel between two cities in any one week to 500 miles.
Develop a summer tour schedule for the band that will maximize totalattendance.

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June July August May 3 4 1 3 4 1 2 3 4 1 2 Capacity 7