Exercise $4\mathrm{.}1$ The Excel spreadsheet $$Exercise $4\mathrm{.}1$ FX model$$ gives crosscurrency exchange rates among the currencies USD, EUR, GBP$,$ AUD, and JPY$.$

Use a linear programming model to detect if these exchange rates contain an

arbitrage opportunity. To do so$,$ use the following decision variables:

xij : amount of currency i converted to currency j$.$

yk: net amount of currency k after all transactions.

Is there an arbitrage opportunity? If the answer is yes, then describe it$,$ for

example: $$Convert $1000$ USD to EUR then to JPY then back to USD to net

$1$ USD without putting money in$.$

$\backslash$table$[[,$USD,EUR,GBP$,$AUD,JPY$],[$USD$,1,0\mathrm{.}639,0\mathrm{.}537,1\mathrm{.}0835,98\mathrm{.}89],[$EUR$,1\mathrm{.}564,1,0\mathrm{.}843,1\mathrm{.}6958,154\mathrm{.}773],[$GBP$,1\mathrm{.}856,1\mathrm{.}186,1,2\mathrm{.}014,184\mathrm{.}122],[$AUD$,0\mathrm{.}9223,0\mathrm{.}589,0\mathrm{.}496,1,91\mathrm{.}263],[$JPY$,0\mathrm{.}01011,0\mathrm{.}00645,0\mathrm{.}00543,0\mathrm{.}01095,1]]$