Reduce file size without reducing print quality for image.

Vector file size in Illustrator is not at all the same thing as raster file size in Photoshop. As a raster image, the file size would normally be much bigger.

You can reduce raster file size by saving out as jpeg, which uses very aggressive data compression - but with a steep price.  Jpeg compression is destructive, non-reversible and cumulative. Depending on circumstances it might not be visually unacceptable as a one-off single output file, but you certainly don't want to replace your original with it.

IIllustrator will allow you to Export .ai files as jpegs.

File > Export As: and choose Jpeg  Here are the options I use. You might choose .png if you need to edit the image and resave it.  Jpeg is "final delivery".

You need to read up on how this DPI/ LPI/ PPI stuff works. File size has nothing to do with it, only the actual dimensions matter in realtion to how finely your printer is actually able to print, meaning the pixel density per print step. If you know the exact target specs of the printer, you can of course tailor your file to it, otherwise adhere to common practices for print production. Other than that I feeel there is no point in going crazy over file sizes. We live in 2018 where storage costs pennies per Gigabyte and Internet transfers can accomodate large files easily even on mobile devices. Being miserly about it just makes no sense.

Mylenium