🚀 go-pugleaf

1> I have just begun to learn Linear Programming model and I come across
a problem which I can't solve.  CAN ANYONE HELP ME, PLEASE?
2> The problem is like this:

There is a currency rates table as follow:

FROM                                             TO
--------------US Dollar---Pound----FFranc----DMark-----Yen
US Dollar-------*--------0.639--- --5.3712----1.5712-----98.8901
Pound--------1.5648-------*--------8.4304----2.459-----154.7733
FFranc-------0.1856-----0.1186------*---------0.2921----18.4122
DMark--------0.6361-----0.4063----3.4233------*---------62.94
Yen----------0.01011----0.00645---0.05431---0.01588-----*

>From the table,
if you use US$ to BUY Pound, then for every US$ 1 you can get 0.639 Pound
if you SELL Pound to get US$, then 0.639 Pound can get US$ 0.639 x 1.5648
    = US$ 0.9999
hence, there is a loss of US$ (1 - 0.9999)
For the above currency transactions, there involve a loss of money.
However, consider this case:
Use US$ 1 to get 0.639 Pound
then use 0.639 Pound to get 0.639 x 8.4304 FFranc
then use 0.639 x 8.4304 FFranc to get 0.639 x 8.4304 x 0.2921 DMark
   i.e. 1.57355 DMark
then use 1.57355 DMark to get US$ 1.57355 x 0.6361
   which is equal to US$ 1.0009
Hence, you can get an extra US$ (1.0009 - 1)

It is required to formulate a LP Decision Model to determine how many
sets of transactions which can get extra money are there in the table.
And identify the transaction sets through the model.

Can anyone help me, please?

Allen
allenyu@netvigator.com