Consider again the CHB Inc. problem described in Problem 10. Suppose only a limted number of PPBs can be placed. CHB would like to place this limited number of PPBs in counties so that the allowable branches can reach the maximum possible population. The file CHBPop contains the county adjacency matrix described in Problem 10 as well as the population of each county.
a. Assume that only a fixed number of PPBs, denoted k, can be established. Formulate a linear binary integer program that will tell CHB Inc. where to locate the fixed number of PPBs in order to maximize the population reached.
b. Suppose that two PPBs can be established. Where should they be located to maximize the population served?
c. Solve your model from part a for allowable number of PPBs ranging from 1 to 10. In other words, solve the model 10 times, k set to 1,2, . . . , 10. Record the population reached for each value of k. Graph the results of part b by plotting the population reached versus number of PPBs allowed. Based on their cost calculations, CHB considers an additional PPB to be a fiscally prudent only if it increases the population reached by at least 500,000 people. Based on this graph, what is the number of PPBs you recommend to be implemented?
CHB, Inc. is 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 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 minimium number of PPB’s required and their location in order to allow CHB to put a branch in every county in Ohio.
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