13 15 10 3 4 15 12 S 8 9 10 Let Ij = Min s.t....

 

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13 15 10 3 4 15 12 S 8 9 10 Let Ij = Min s.t. + + + + + Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Node 7 Node 8 Node 9 Node 10 1 if the are from node i to node j is on the shortest route 10 otherwise 8x12 + 15 ✓X27 + 3X46+ 4X67 + 2X78 + 12 ✓ X95 + 1✔ X12 + 1 ✔ X23 + 1 ✔ X32 + 1x43 + 1 ✔ X54 + 1 ✓x63 + 1 X69 1 ✔ X72 + 1x06+ 1x95 + 13X13+ 5x32 + 4 ✔ X54 + 2 ✓ X68 + -1 X X70 + 5 ✔ X96 + 1 ✓x13+ 1 ✓ X27 1 ✓X30 1 1 ✔ X59 1 ✔ X64 + Flow Out ✓X45 + 15 ✔ X14 + 5 ✔ X36 + 12 ✔ XS9+ 5 ✔ X69 + 1 √x76+ 1 ✓X09 + 1 ✔ X96 + 2 x86 + 5 ✔ X98 + 1 ✓ X14 + 1 ✓ X46 1 ✔ X67 + 1 ✔ X78 + 1 ✓X80 1 ✓ x90 + 10 ✓X15 + 2X43 + 5 ✔ X63 + 15 ✓X72 + 5x89 + 0 x x90 1 ✔ X15 1 ✓X60 + 1 ✓ X70 1 X90 5X23 4X45 3 X64 ✓ 4X76 8 X X50 + + + + + + + + -1 ✓x12 + -1 ✔ X13 + -1 ✓X14 + -1 ✔ X15 + -1 ✔ X36 + X96 -1 ✓X27 + -1X60 + -1 ✓X59 + 1 ✔ X70 + Xij 20 for all / and / Flow In -1 ✓X32 + -1 ✓X23 + -1 ✓X54 + -1 ✓X45 + -1 ✓X4G+ -1 ✓X67 -1 ✓X70 + -1 ✓X69 + 1 V XEO t -1 ✓x72 -1X43 + -1 ✓ X64 -1 ✓ X95 ✓X76 + -1 -1 ✓ X90 -1 ✓ X89 ✓ X90 1 -1 ✓X63 -1 ✓ XDG + = - = = ☐☐☐☐☐ Optimal Solution: Variable Value X12 X13 X14 XXX X15 X23 X27 X32 X36 X43 X45 X46 X54 X59 X X X X63 X64 X67 X68 X69 X72 X76 X78 X70 X86 X89 X80 X95 X96 X78 X70 X86 X89 X80 X95 X96 X98 X90 Shortest Route: Total Time = minutes 1-5-4-6-7-10 1-5-9-10 1-3-4-6-7-10 1-2-7-10 1-2-3-6-7-10 1-3-6-8-7-10 13 15 10 3 4 15 12 S 8 9 10 Let Ij = Min s.t. + + + + + Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Node 7 Node 8 Node 9 Node 10 1 if the are from node i to node j is on the shortest route 10 otherwise 8x12 + 15 ✓X27 + 3X46+ 4X67 + 2X78 + 12 ✓ X95 + 1✔ X12 + 1 ✔ X23 + 1 ✔ X32 + 1x43 + 1 ✔ X54 + 1 ✓x63 + 1 X69 1 ✔ X72 + 1x06+ 1x95 + 13X13+ 5x32 + 4 ✔ X54 + 2 ✓ X68 + -1 X X70 + 5 ✔ X96 + 1 ✓x13+ 1 ✓ X27 1 ✓X30 1 1 ✔ X59 1 ✔ X64 + Flow Out ✓X45 + 15 ✔ X14 + 5 ✔ X36 + 12 ✔ XS9+ 5 ✔ X69 + 1 √x76+ 1 ✓X09 + 1 ✔ X96 + 2 x86 + 5 ✔ X98 + 1 ✓ X14 + 1 ✓ X46 1 ✔ X67 + 1 ✔ X78 + 1 ✓X80 1 ✓ x90 + 10 ✓X15 + 2X43 + 5 ✔ X63 + 15 ✓X72 + 5x89 + 0 x x90 1 ✔ X15 1 ✓X60 + 1 ✓ X70 1 X90 5X23 4X45 3 X64 ✓ 4X76 8 X X50 + + + + + + + + -1 ✓x12 + -1 ✔ X13 + -1 ✓X14 + -1 ✔ X15 + -1 ✔ X36 + X96 -1 ✓X27 + -1X60 + -1 ✓X59 + 1 ✔ X70 + Xij 20 for all / and / Flow In -1 ✓X32 + -1 ✓X23 + -1 ✓X54 + -1 ✓X45 + -1 ✓X4G+ -1 ✓X67 -1 ✓X70 + -1 ✓X69 + 1 V XEO t -1 ✓x72 -1X43 + -1 ✓ X64 -1 ✓ X95 ✓X76 + -1 -1 ✓ X90 -1 ✓ X89 ✓ X90 1 -1 ✓X63 -1 ✓ XDG + = - = = ☐☐☐☐☐ Optimal Solution: Variable Value X12 X13 X14 XXX X15 X23 X27 X32 X36 X43 X45 X46 X54 X59 X X X X63 X64 X67 X68 X69 X72 X76 X78 X70 X86 X89 X80 X95 X96 X78 X70 X86 X89 X80 X95 X96 X98 X90 Shortest Route: Total Time = minutes 1-5-4-6-7-10 1-5-9-10 1-3-4-6-7-10 1-2-7-10 1-2-3-6-7-10 1-3-6-8-7-10

Answer rating: 100% (QA)

Solution Shortest route 1546710 Total time 25 minutes Let zy Min st Node 1 Node ... View the full answer