24x36 @ 300 dpi is 222Mb uncompressed. So it ought to be smaller than that as a file to send to print. Also, if it gets a silly size then draw one in vector format and send as a PDF which would be a lot smaller.

Even so, 200Mb is large but its still within FTP ability. At 32K byte per sec upload that's about 2hrs. Ok you can forget it with a dialup modem tho.