You are given the following exchange rates;

1 Pound = 1.645 US $

1 US $ = 1.325 Australian $

1 Australian $ = 0.305 British Pound.

Assume you have US $10,000. Is there a way for you to profit from any arbitrage opportunities that may exist given these exchange rates. Assume a US $10 transaction cost per currency exchange (regardless of amount), to paid at the end of all transactions. Show all work clearly.