In this problem we will discover how you, too, can be employed by Wall Street and cause a major economic collapse! The arbitrage business is a money-making scheme that takes advantage of differences in currency exchange. In particular, suppose that 1 US dollar buys 120 Japanese yen; 1 yen buys 0.01 euros; and 1 euro buys 1.2 US dollars. Then, a trader starting with $1 can convert his money from dollars to yen, then from yen to euros, and finally from euros back to dollars, ending with $1.44! The cycle of currencies is called an arbitrage cycle. Of course, finding and exploiting arbitrage cycles before the prices are corrected requires extremely fast algorithms. Suppose n different currencies are traded in your currency market. For each currency i and currency j, one unit of currency i can be traded for r_i, j units of currency j. (Do not assume that r_ij = r_ji.) For the given exchange rates, you want to find a cycle that starts and ends with USD, for which you can make a profit through exchanges. There might not be such a cycle. If there are multiple profitable cycles, you want to find the most profitable. To satisfy both your company's and SEC regulations, you should only trade each non-USD currency at most once. This means dollars rightarrow euro rightarrow rubles rightarrow yen rightarrow dollars is ok, but not dollars rightarrow euro rightarrow rubles rightarrow euros rightarrow yen rightarrow dollars. Cast this problem as a min-cost network flow problem (MCNFP) LP. Define the nodes, edges, and all parameters for the MCNFP in terms of the original problem. Draw an example network (with all parameters) for the case of just three currencies: dollars, yen, and euro