12. CHB, Inc., a bank holding company, 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 file CHB contains an adjacency matrix with a one in the ith row and jth column indicating that the counties represented by the ith row and the jth column share a border. A zero indicates that the two counties do not share a border. Formulate and solve a linear binary model that will tell CHB the minimum number of PPBs required and their location in order to allow CHB to put a branch in every county in Ohio.

SHOW ON EXCEL

Ohio Ohio 20 39 78 2 18 758 60 61 76 77 21 38 40 37 411 (36| 42 | 57 59 75 23 62 63 3543 56 55 54 66 7 Ohio Ohio 20 39 78 2 18 758 60 61 76 77 21 38 40 37 411 (36| 42 | 57 59 75 23 62 63 3543 56 55 54 66 7