Suppose that we have N different currencies (e.g., US Dollars, Euros, etc.). For each pair of currencies, (i, j), one unit of currency i can be exchanged into rij units of currency j. We wish to find an arbitrage opportunity if it exists, i.e., a sequential series of currency trades that allows us to make a profit with no risk. Formulate this as a min-cost flow problem and provide an LP with a bounded feasible polytope which solves it. Assume no transaction costs.