Final Fantasy XIV Database - Ffxivpro.com

I'm fairly confident in saying you'd be losing a lot of money doing that. Gold Ingot's sell for 15k per on my server, turn that into 6 arrowheads, then turn the arrowheads into 2 stacks of arrows.

The arrows would have to sell atleast 75 gil each in order to make your money back. And this isn't taking into factor the cost of the copper ingot, crystals, the materials needing to turn the arrowheads into arrows.. you'd need the arrows to sell for probably 90-100 gil per to make your money back.

And I am only assuming, but I'd estimate the actual in-game resale value at about 10-15 gil.

Don't do it. And if you still want to, do only one synth then. Synth 1 gold ingot into arrowheads, then the arrowheads into arrows, then see how much they sell for.