Consider the following two congestion networks with the indicated cost functions for a flow \(x\) on the respective edge; for example, \(50+x\) is short for \(c(x)=50+x\). Note that different edges may have different flows \(x\) that depend on the chosen routes by the users.

Suppose there are six users who want to travel from \(o\) to \(d\).

(a) Find the equilibrium flow in the network on the left.

(b) In the network on the right, start from the equilibrium flow in

(a) and improve the route of one user at a time until you find an equilibrium flow. Compare the equilibrium costs in both networks.

50+x 10x P 10x 50+ x d 50+x 10x 10+x = 10x 50+x