Problem $3$: In this exercise, we show how to solve the currency problem from Problem $2$ by giving an algorithm based on the solution of a min$-$cost flow LP that, given a network $\backslash ($ N$($V$,$ A$)\backslash )$ with costs $\backslash ($ c: A $\backslash$rightarrow $\backslash$mathbb$\{$Z$\}\backslash )$ on the arcs, finds a cycle of negative cost in the network, or concludes that no such a cycle exists.