# problem 2 a suppose that we have n different currencies e g us dollars euros etc for 5176078 Problem 2 (a) 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. (b) Can you find an arbitrage opportunity given the currency exchange rates in the spreadsheet “curren- cies.xlsx”? If so, describe the corresponding trades. What is the maximum amount of profit that can be made for each \$1.00 invested in this procedure? (e) Suppo e now that the exchange charges a p% transaction fee on each unit of currency traded. In other words, if we wish to trade currency i into currency J, p% of our initial amount of l is taken away before doing the exchange. Modify your LP from (a) to take these fees into account. Asuming p 0.50, how does this change your answer for (b)?