What resolution do I need for print?
You need the file made for the size of the piece, menu or banner, not a small social export. If you only have the feed jpg, it does not reach paper: it looks soft as soon as it is enlarged.
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Ask the printer for the final size before you commission that version. The miss in Madrid is printing the website screenshot on the table menu. When print is in the uses, that version goes separately, at the size of the piece, as well as the screen file.