Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 7H / a / Solution

The dual pair
$$
\min\{c^Tx:Ax\geq b,\ x\geq0\}
\quad\hbox{and}\quad
\max\{b^Ty:A^Ty\leq c,\ y\geq0\}
$$
satisfies weak duality because $b^Ty\leq y^TAx=x^TA^Ty\leq c^Tx$ for every feasible pair.


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 Incoming links: Dual of a minimization linear program in inequality form