2. Sites Selection An owner of a motel chain seeks to expand its business. The owner has identified nine potential locations where a motel might be located. However, some of these locations are within 30 miles of each other, and the owner prefers to separate motels in the chain by at least 30 miles to avoid cannibalizing demand. The information about location conflicts has been obtained from a map: Potential site 1 2 1 2 3 4 5 3 4 7 8 9 5 6 1 1 1 7 8 9 (a) [5pts] The owner wants to build motels on as many sites as possible, while adhering to the 30-mile requirement. Which sites should be selected? Potential sites within 30 miles Hint: we can build the table for the conflicts: the numbered rows and columns correspond to the various motel sites. An entry of 1 appears in row i and column j if sites i and j are within 30 miles of each other. 2 1, 5, 7 5, 6, 8, 9 6, 7 2, 3, 6, 8 3, 4, 5, 7 1 2, 4, 6 3, 5 2 3 4 5 1 1 1 1 1 6 7 8 9 1 1 1 1