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?

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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 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.
Click on the datafile logo to reference the data.
DATA file
OHIO
19
20
80
39
78
40
18
38
81
21
77
37
41
01
76
3
17
82
22
59
30
42
02
16
57
75
83
23
15
35
03
84
43
50
74
24
14
04
85
34
44
25
13
73
87
45
20
33
12
54
72
27
88
07
45
32
11
28
53
71
47
08
52
31
10
48
51
29
30
49
TC
70
50
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
Transcribed Image Text: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 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. Click on the datafile logo to reference the data. DATA file OHIO 19 20 80 39 78 40 18 38 81 21 77 37 41 01 76 3 17 82 22 59 30 42 02 16 57 75 83 23 15 35 03 84 43 50 74 24 14 04 85 34 44 25 13 73 87 45 20 33 12 54 72 27 88 07 45 32 11 28 53 71 47 08 52 31 10 48 51 29 30 49 TC 70 50 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
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