Let $X$ and $Y$ be nonempty sets, let $c: X \times Y \to \mathbb{R}$ be a cost function, and let $\varphi: X \to \mathbb{R}$ and $\psi: Y \to \mathbb{R}$ be functions. Suppose that $(\varphi,\psi)$ is admissible, meaning that $\varphi(x) + \psi(y) \leq c(x,y)$ for every $x \in X$ and every $y \in Y$. Define the $c$-transforms $\varphi^c: Y \to \mathbb{R} \cup \{-\infty\}$ and $\psi^c: X \to \mathbb{R} \cup \{-\infty\}$ by $\varphi^c(y) := \inf_{x \in X}\{c(x,y) - \varphi(x)\}$ for every $y \in Y$, and $\psi^c(x) := \inf_{y \in Y}\{c(x,y) - \psi(y)\}$ for every $x \in X$. Then $\psi(y) \leq \varphi^c(y)$ for every $y \in Y$, and $\varphi(x) \leq \psi^c(x)$ for every $x \in X$.