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Take the file to a print show that support Illustrator or PDF files, and save as press ready PFD. If the print shop says they only print JPEG and you must print there (I wouldn't) then use File > Export rather than Save for Web. Save for Web is for saving for.... Web. Really?
Go to Effects>Document Raster Effects Settings and either check high Quality 300 DPI or do a custom setting and use 355 dpi which is what the high end publications use.
Then make your pdf and that should do it. The 72 dpi is a way of keeping the file smaller and have illustrator function faster. It is the default setting.
When you save the file as .jpg there is a dialog that opens that allows you
to set the resolution. 72 is the (old) standard for internet images because
older monitors worked at 72hz and pixels were scanned 1/1 at that rate.
With today's falt screen monitors, scan rate is a thing of the past so only
pixel count size is relevant fro web display. For print, simply set the dpi
to high (300) or more (custom).
Also, you'll need to discus with the print shop what formats thay like to
use best. .jpg is not often used for print, CMYK .tiff is used more often
along with .pdf production ready.