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is integral if For each and every bounded possible integral aim operate c, the exceptional value of the linear program max c x ∣ x ∈ P displaystyle max cxmid xin P

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max c T x ∣ x ∈ R n ∧ A x ≤ b ∧ x ≥ 0 displaystyle max ,mathbf c ^ mathsf T mathbf x mid mathbf x in mathbb R ^ n land Amathbf x leq mathbf b land mathbf x geq 0,

Its objective function is a real-valued affine (linear) perform described on this polytope. A linear programming algorithm finds a degree while in the polytope in which this perform has the most important (or smallest) benefit if this sort of a point exists.

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It is possible to obtain an exceptional Answer to the twin when only an exceptional Remedy towards the primal is known using the complementary slackness theorem. The theorem states:

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