A Central Result of LP TheoryDuality Theorem
Every linear program has a dual
If the original is a minimization, the dual is a maximization and vice versa
Solution of one leads to solution of other
Primal: Minimize cx subject to Ax >= b, x>=0
Dual: Maximize yb subject to yA <=c, y>=0
If one has optimal solution so does other, and their values are the same.