CaroliNet is a satellite TV service provider for residential customers in the state of North Carolina. The company is planning to expand and offer satellite TV service in South Carolina as well. The company wants to establish a set of service hubs throughout the state in such a way to ensure that all residents of the state have a service hub either in their own country or in an adjacent county. Figure 6.44 (and the file CaroliNet.xlsm that accompanies this book) show an Excel spreadsheet with a matrix indicating county adjacencies throughout the state. That is, values of 1 in the matrix indicate counties that are adjacent to one another while values of 0 indicate counties that are not adjacent to one another.

a. Assume CaroliNet wants to minimize the number of hubs they must install. In what counties should the hubs be installed?

b. Suppose CaroliNet is willing to install hubs in exactly 10 different counties. In what counties should the hubs be installed if the company wants to maximize its service coverage?

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