An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 8

CHB, Inc. Is a bank holding company that is evaluating the potential for expanding into a 13-county region in the south western part of the 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.
a. Assume that only one PPB can be established in the region. When.' should 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 y i = 1 if it is not possible to establish a branch in county i and y i. = 0 otherwise.)b. Suppose that two PPBs 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. It' CUB 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 adv ice would you give the management of CHB?