Question: (a) Formulate the problem as an LPP by considering decision variables Xij = 1 if i j is in the shortest path and zero otherwise.

(a) Formulate the problem as an LPP by considering decision variables Xij = 1 if i j is in the shortest path and zero otherwise. ( Keep your formulation such that every variable has a positive coefficient in one constraint (for source node) and a negative coefficient in another (for sink node). )

(b) Write the dual to part (b) considering all Xij 0

(a) Formulate the problem as an LPP by

1. A person located in City l wants to reach City 5. Figure shows the network, connecting the cities along with the time taken to travel. The problem is to determine the path that takes the shortest time to travel from City 1 to City 5. (2 7 8 5 4 5 1 6 3 10 3 (a) Formulate the problem as an LPP by considering decision variables Xij = 1 if i- j is in the shortest path and zero otherwise. (Keep your formulation such that every variable has a positive coefficient in one constraint (for source node) and a negative coefficient in another (for sink node). ) (b) Write the dual to part (b) considering all Xij > 0

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