A 6-node network with the following list of distances between various pairs of nodes: From Node To Node Distance 1 2 90 1 3 80 2 4 70 2 5 30 3 4 40 3 5 50 4 5 40 4 6 60 5 6 90 10a Formulate finding the shortest route from node 1 to node 6 as a linear programming problem. Please list all nodes that are coming in and out that equal to 0 10b Solve the problem on a linear programming software and show the total distance and the connections from node 1 to node 6 for the shortest route.
Added by David B.
Step 1
The objective is to minimize the total distance: Minimize: \( 90x_{12} + 80x_{13} + 70x_{24} + 30x_{25} + 40x_{34} + 50x_{35} + 40x_{45} + 60x_{46} + 90x_{56} \) Subject to: - \( x_{12} + x_{13} = 1 \) (Node 1 can only connect to either Node 2 or Node 3) - \( Show more…
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