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The challenge of fixing a system of linear inequalities dates back again at the least so far as Fourier, who in 1827 published a way for solving them,[one] and soon after whom the tactic of Fourier–Motzkin elimination is named.

Geometrically, the linear constraints outline the possible location, and that is a convex polyhedron. A linear perform is usually a convex functionality, which suggests that each nearby least is a world minimal; in the same way, a linear function is really a concave function, which implies that every neighborhood highest is a global maximum.

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