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 (-). Min x12 + x13 + x14 + x23 + x25 + x32 + x35 + x46 + x52 + x53 + x56 + x57 + x65 + x67 s.t. Flow Out Flow In Node 1 x12 + x13 + x14 = Node 2 x23 + x25 + x12 + x32 + x52 = Node 3 x32 + x35 + x13 + x23 + x53 = Node 4 x46 + x14 = Node 5 x52 + x53 + x56 + x57 + x25 + x35 + x65 = Node 6 x65 + x67 + x46 + x56 = Node 7 + x57 + x67 = xij ≥ 0 for all i and j Optimal Solution: Variable Value x12 x13 x14 x23 x25 x32 x35 x46 x52 x53 x56 x57 x65 x67 Shortest Route: 1-2-5-6-7 Length =
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The objective is to minimize the sum of the variables representing the flow on each edge (x12, x13, x14, etc.), where each variable represents the flow on a direct path between two nodes (e.g., x12 is the flow from node 1 to node 2). Show more…
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Considering the network below, calculate the shortest paths to all nodes from source node A using Dijkstra's algorithm. In choosing the node to explore next, if there is more than one candidate, choose the one alphabetically earlier first. - A few entries for Iteration 1 are filled out. Use a similar format for your answers. For each iteration: - "Distance" means the shortest known distance from the source node A to this particular node. - "From" means the preceding node of this particular node in the shortest known distance path. - "Finalized?" means is the shortest distance path from the source node to this particular node finalized? Iteration 1
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