We present a formula for the optimal value ƒc(y) of the integer program max {c′x| x ∈ Ω(y)∩ℕn} where Ω(y) is the convex polyhedron {x ∈ ℝn| Ax = y, x ≥ 0}. It is a consequence of Brion and Vergne's formula which evaluates the sum ∑x∈Ω(y)∩ℕnec′x. As in linear programming ƒc(y) can be obtained by inspection of the reduced costs at the vertices of the polyhedron. We also provide an explicit result that relates ƒc(ty) and the optimal value of the associated continuous linear program for large values of t ∈ ℕ.
