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Is there a general formula for image size vs. print size?
I have a wonderful photo from my cell phone and several people would like a 16x20 or at the least a 11x14 print. When I upload to mpix it is only letting me print basically half of my print.
It's possible, but Mpix is trying to protect you from yourself. Your camera's 8 megapixels make an image with something like 2448 × 3264 pixels. That means that when you print an image 16 inches wide, you end up with about 150 pixels per inch. If you look closely, you may see some blockiness, and the phone camera's image quality probably isn't such that it stands up to high scrutiny. General guidelines suggest 300 pixels per inch for the best quality, and it looks like your print service is enforcing that. That's because they don't want you to use their service and then complain about poor results even when it's not their fault.
However, if you understand the limitations and aren't expecting more than is possible, you may be perfectly happy with a 150dpi print. If you normally look at it from a reasonable viewing distance rather than up close, this should be just fine. Your print service may have an advanced setting where you tell them "I understand what I'm doing; please go ahead anyway." If they don't, you can use an image editing program to scale up the image to 4× the size (twice in every direction). This will make the file much bigger and not increase quality at all — but should fool the artificial restrictions.
While it is possible, the quality will suffer. The general recommendation is that photos be printed at at least 300 dots per inch or pixels per inch. At 8mp, this will not quite fill an 8 by 11 sheet of paper. You could print at 150 ppi and just barely get a 16 by 20, but the quality would likely be noticeably lower up close.
Resize and crop your image to 3000x2400px with 150dpi which is 16x20. By that way printing app will see your photo as 16x20 , if the problem still persists probably the app reads resolution/300dpi so you need to enlarge the size to 6000x4800px with 300dpi which is a bit problematic because you will lose quality but the printing app will recognize it for sure by this. You can surely resize better in Lightroom and Photoshop. After resize you can give a little sharpen to your image to enhance.
Also for printing quality optimization if you can choose paper type my recommendation to you is
if the printing system is analog, paper selection shall be silk(e-type) if the printing system is digital, paper selection should be lustre or fine-art.
