Past exam of the mathematics course of the University of Cambridge / 2005 / ib / Paper 3 / 20D / b / Solution

The dual linear program isThe negatives of the final slack payoff coefficients give $\boxed{y^{\ast }=(1,2/3,2/3)}$. Its three dual constraints are equalities, and its objective is $11+32/3+58/3=41$. Equality with the primal objective proves optimality by weak duality, independently of tableau sign conventions. It is also the complementary slackness certificate, with all primal variables and all dual variables strictly positive.