CHB, Inc., is a bank holding company that is evaluating the potential for expanding into 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 (principle place of business) is located. The following map shows the 13-county region, with the population of each county indicated:a. Assume that only one PPB can be established in the region. Where should it be located to maximize the population served? 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 otherwiseb. Suppose that two PPB’s can be established in the region. Where should they be located to maximize the population served?c. Management learned that a bank located in county 5 is considering selling, If CHB purchases this bank, the requisite PPB will be establshed in county 5, and a base for beginning expansion in the region will also be established. What advice would you give the management of CHB?
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