CHB, Inc., a bank holding company that is evaluating the potential for expanding into the state of Ohio. State law permits establishing branches in any county that is adjacent to a county in which a PPB (principal place of business) is located. The following map shows the State of Ohio. The DATAfile CHB contains an adjacency matrix with a one in the i^th row and j^th column indicating that the counties represented by the i^th row and the j^th column share a border. A zero indicates that the two counties do not share a border.

Click on the datafile logo to reference the data.

Solve a linear binary model that will tell CHB the minimum number of PPB's required and their location in order to allow CHB to put a branch in every county in Ohio.

The first solution places PPBs in the following counties: 8,14,17,19,29,33,35,38,51,55,59,68,75,78,87.

Use the procedure for finding an alternative solution to determine if the above solution is unique. How many alternative optimal solutions are there?