A renowned money market trader, Mr. Wilkinson, often finds profitable arbitrage transactions in foreign currencies. Suppose that he faces possible trades in seven different currencies (US$, , , Yuan, Bhat, S$, HK$). Let x,, be the amount of currency i that Wilkinson sells in exchange for currency j, and r, be the exchange rate. For example, r = 115 indicates that for each US$ he sells, he can obtain 115 . Assume that with rapid communications, Wilkinson knows the current values of all r, at any moment, and that he can execute virtually simultaneous exchange agreements. The only requirement on Wilkinson is that he is not short on any currency. In other words, he should atleast be able to cover the total sales of each currency with the proceeds coming from any of the other exchanges that yield that currency. Wilkison seeks a set of currency exchanges that yield a profit measured in US$. Formulate an appropriate mathematical model.