Problem: CHB, Inc., is a bank holding company that is evaluating the potential for expanding into a 13-county region in the southwestern part of the state. 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 13-county region with the population of each county indicated.
1) Assume that only one PPB can be established in the region. Where should it be located to maximize the population served? (Hint: Review the Ohio Trust formulation in Section 7.3. Consider minimizing the population not served, and introduce variable yi = 1 if it is not possible to establish a branch in county i, and yi = 0 otherwise.)
2) Suppose that two PPBs can be established in the region. Where should they be located to maximize the population served?
3) Management learned that a bank located in county 5 is considering selling. If CHB purchases this bank, the requisite PPB will be established in county 5, and a base for beginning expansion in the region will also be established. What advice would you give the management for CHB?