Setting a minimum filesize whilst fixing the image width and height is silly. If you don't use compression then the filesize is determined by the image dimensions. And if you do use compression then the filesize is determined by the level of entropy (disorder) in the image.
Some images have higher entropy because there is more going on, more detail etc. in the image. Some images have very low entropy because there are large areas with little detail, such as skies, or plain backgrounds. So it makes no sense to impose a minimum filesize because it depends on what sort of image yon have!
But if some deranged person was holding a gun to your head insisting that you make your 305mm X 203mm 300dpi image at least 10 megabytes then you could use lossless compression and add an increasing level of noise until you hit the desired filesize (noise is by definition uncompressable with lossless schemes such as LZW). If you're over 25MB then you can in a similar fashion reduce the filesize by repeatedly applying a blur with a small radius.
Personally I think this lower limit must be some sort of mistake as altering your image in this way to increase the size doesn't really do anything to improve image quality (unless you have posterization, but that's another story!)