Farka's Lemma and Linear Programming Duality

1. Farka's Lemma

Let and Then exactly one of the following two statements is true:
(1). There exists an such that and
(2). There exists a such that and
Proof:

• (1) feasible to show (2) infeasible is trivial.
• (1) infeasible to show (2) feasible is by separation theorem.

Note
(2) can be written in the following way
There exists a such that and

2. Linear Programming Primal-Dual table

primal_dual_table.png

Example:
Primal:

Dual: