Question

A) Write another way of modeling the max flow as a linear program by defining variables...

A) Write another way of modeling the max flow as a linear program by defining variables for each s-t path. What is an interpretation of this
LP?

B)  What is the dual of the above LP? What is an interpretation of the LP?
This shows that there may be multiple LP formulations of a problem

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Answer #1

A)

B) Dual of LP:

The dual of linear program (LP) is another LP that is derived from the original the primal LP.

Each variable in the primal LP becomes a constraint in the dual LP.

Each constraint in the primal LP becomes a variable in the dual LP.

The objective direction is inversed maximum in the primal becomes minimum in the dual and vice versa.

The weak duality theorem states that the objective value of the dual LP at any feasible solution is always a bound on the objective of the primal LP at any feasible solution upper or lower bound, depending of wheather it is a maximization or mi nimization problem. In fact, this bounding property holds for the optimal values of the dual and primal LPs.

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