Question: Problem 6-23 (Algorithmic) Find the shortest route from node 1 to node 7 in the network shown. If the constant is 1 it must be

Problem 6-23 (Algorithmic) Find the shortest

Problem 6-23 (Algorithmic) Find the shortest route from node 1 to node 7 in the network shown. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". For negative values enter "minus" sign (-). 6 12 6 18 6 4 3 18 3 3 Let Iij 1 if the arc from node i to node j is on the shortest route otherwise Min 1 X X12 + 13 X X13 + 18 X X14 + 3 X X23 + 5 X X25 + 3 X X32 + 4 X X35+ 3 / 146 + 5 X X52 + 4 X X53 + 2 X X56 + 6 X X57 + 2 X X65 + 3 X X67 Flow Out Flow In Node 1 1 x12 + 1 13+ 1 x14 + -1 x32 + Node 2 1 X23 + 1 X25 -1 X12 + -1 X52 + -1 X23 + Node 3 1 x32 + 1 X35 -1 X13 + -1 X53 Node 4 14x46 + -1 V X14 1 X53 + 1 X56 + + -1,x25 + -1 X35+ Node 5 1 x52 + 1 x57 -1 x65 Node 6 1 X65 + 1 X67 + -1/x46 + -1 X56 Node 7 1 X57 + 1 x67 Xij 2 0 for all i and Optimal Solution: Variable Value X12 X13 X14 X23 X25 X32 X35 X46 X52 X53 X56 X57 X65 X67 Shortest Route: 1-4-6-7 Length = 17

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