(6 points) Shortest paths can be cast as an LP using distances dv from the source to a particular vertex variables. We can compute the shortest path from $ to t in a weighted directed graph by solving: max dt subject to ds = 0, dv du < wlu,v) for all (u,v)eE. We can compute the single-source by changing the objective function to max Evev dv.
Use linear programming to answer the questions below. State the objective function and constraints for each problem and include a copy of the LP code and output:
a) Find the distance of the shortest path from vertex 0 to vertex 7 in the graph below.
b) Find the distances of the shortest paths from vertex 0 to all other vertices.
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