PLEASE READ THE ENTIRE QUESTION. I am looking to find out how many alternative optimal solutions are there. I am not looking for any other answer. The answer is NOT 15.
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CHB, Inc., 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 DATAfile CHB contains an adjacency matrix with a one in the th row and th column indicating that the counties represented by the throw and the jth column share a border. A zero indicates that the two counties do not share a border. Click on the datafile logo to reference the data. DATA file OHIO 19 20 79 30 1 78 2 18 38 40 80 52 81 21 77 37 41 81 78 3 17 82 22 59 38 4 42 62 16 57 75 33 23 5 15 35 63 84 74 24 50 86 PL 44 36 64 34 85 25 13 73 87 20 86 33 12 54 27 66 72 88 81 32 11 53 8 28 71 47 68 52 9 31 10 45 69 51 22 30 TO 70 30 Solve a linear binary model that will tell CHB the minimum number of PPB's required and their location in order to allow CHB to put a branch in every county in Ohio. The first solution places PPBs in the following counties: 8,14,17,19,29,33,35,38,51,55,59,68,75,78,87. Use the procedure for finding an alternative solution to determine if the above solution is unique. How many alternative optimal solutions are there? 15 CHB, Inc., 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 DATAfile CHB contains an adjacency matrix with a one in the th row and th column indicating that the counties represented by the throw and the jth column share a border. A zero indicates that the two counties do not share a border. Click on the datafile logo to reference the data. DATA file OHIO 19 20 79 30 1 78 2 18 38 40 80 52 81 21 77 37 41 81 78 3 17 82 22 59 38 4 42 62 16 57 75 33 23 5 15 35 63 84 74 24 50 86 PL 44 36 64 34 85 25 13 73 87 20 86 33 12 54 27 66 72 88 81 32 11 53 8 28 71 47 68 52 9 31 10 45 69 51 22 30 TO 70 30 Solve a linear binary model that will tell CHB the minimum number of PPB's required and their location in order to allow CHB to put a branch in every county in Ohio. The first solution places PPBs in the following counties: 8,14,17,19,29,33,35,38,51,55,59,68,75,78,87. Use the procedure for finding an alternative solution to determine if the above solution is unique. How many alternative optimal solutions are there? 15
