= Solution
The <dual linear program> is
$$
\boxed{\begin{aligned}\text{minimize }&11y_1+16y_2+29y_3,\\\text{subject to }&-3y_2+9y_3\geq4,\\&y_1+2y_2-2y_3\geq1,\\&-11y_1-7y_2+10y_3\geq-9,\\&y_1,y_2,y_3\geq0.\end{aligned}}
$$
The negatives of the final slack payoff coefficients give $\boxed{y^*=(1,2/3,2/3)}$. 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.
Back to article page
