Statement
Lemma
A linear programme (given by
, and ) has an optimal point if and only if its dual linear programme has an optimal point . These relate by
Proof
From the Strong duality theorem (linear programme) we know the original linear programme is feasible and bounded if and only if the dual linear programme is feasible and bounded.
However, a linear programme has a solution if and only if it is feasible and bounded therefore providing the equivalence above.
The relationship between the points is given by the weak duality theorem. This is not finished