is alleged to generally be integral if for all bounded possible goal functions c, the linear method max c x ∣ x ∈ P displaystyle max cxmid xin P

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Geometrically, the linear constraints outline the possible area, and that is a convex polytope. A linear function is often a convex functionality, which suggests that every nearby minimum is a world minimum amount; likewise, a linear operate is often a concave operate, which implies that each area most is a global optimum.

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A pictorial illustration of an easy linear program with two variables and 6 inequalities. The set of feasible remedies is depicted in yellow and varieties a polygon, a 2-dimensional polytope.

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Find a vector x that maximizes c T x issue to the x ≤ b and x ≥ 0 . displaystyle begin aligned & text Find a vector &&mathbf x & text that maximizes &&mathbf c ^ mathsf T mathbf x & textual content subject to &&Amathbf x leq mathbf b & textual content and &&mathbf x geq mathbf 0 .conclude aligned

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