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Dual of a minimization linear program in inequality form

The dual pair

min {c^{T} x : A x \geq b, x \geq 0} and max {b^{T} y : A^{T} y \leq c, y \geq 0}

satisfies weak duality because

b^{T} y \leq y^{T} A x = x^{T} A^{T} y \leq c^{T} x

for every feasible pair.

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Solution