LP Duality and max-flow min-cut theorem

In this exercise, we will demonstrate that LP duality can be used to show the max-flow min-cut theorem Consider this instance of max flow: 4 4 Let fl be the flow pushed on the path (S,A,T), f2 be the flow pushed on the path S, A, B,T), and fs be the flow pushed on the path {S, B,T). The following is an LP for max flow in terms of the variables f,.fa: max fi +f2+f3 (Constraint for (S, A)) (Constraint for (S, B)) (Constraint for (A, T)) (Constraint for (A, B)) (Constraint for (B,T)) The objective is to maximize the flow being pushed, with the constraint that for every edge, we can't push more flow through that edge than its capacity allows. In this exercise, we will demonstrate that LP duality can be used to show the max-flow min-cut theorem Consider this instance of max flow: 4 4 Let fl be the flow pushed on the path (S,A,T), f2 be the flow pushed on the path S, A, B,T), and fs be the flow pushed on the path {S, B,T). The following is an LP for max flow in terms of the variables f,.fa: max fi +f2+f3 (Constraint for (S, A)) (Constraint for (S, B)) (Constraint for (A, T)) (Constraint for (A, B)) (Constraint for (B,T)) The objective is to maximize the flow being pushed, with the constraint that for every edge, we can't push more flow through that edge than its capacity allows