Existence of an Optimal Plan for the Finite Kantorovich Problem is a result from the foundations of optimal transport. For mathematical objects. Let mathematical objects and mathematical objects satisfy i=1m ai = 1 and j=1n bj = 1. Let mathematical objects. Define the finite transport polytope (a,b) := \P = (Pij) [0,)m n : j=1n. It helps organize the relationship between Monge maps, Kantorovich plans, duality, and Wasserstein geometry.