It obviously depends on what the G.E prices of what you are buying.
Yew long (u) 396 Gp
Bow String 186
= 582 to make a Yew longbow finished
Yew longbow 666 Gp
So you would make 84 gp profit(or something like that) for each bow you make
BUT
If you wait too long to sell them, the G.E could update and you could dramatically lose profit, So if the price of Yew longs go down lower than 582 before you sell them, than you are going to lose profit of course.
It all depends on how fast you can make and then sell the bows.
Edit: These are the prices as of 6/7/11