Consider finding the shortest path route from node 1 to node

Consider finding the shortest path route from node 1 to node 3. Formulate it as a linear programming problem. Take the arc in the order {(1, 2), (1,4), (2,3), (3, 4), (4, 5), (5, 3)}. (hint: Formulate as min c\'x subject to Ix = b. . x > 0. and identify c, I and b.

Solution

shortest path from 1 to 3

is (1,4) (4,2) with 3

or (1,4) (4,5) (5,3) = 3

Others are having more values

3 is the minimum value and any one of the two routes is the shortest of all.