So the engineering firm's PDF probably consists of a mix of vector imagery which can be quite efficient since vector typically only stores points of interest, not the whole scene. So a simple vector image of a line on a white square might get away with a few bytes for the two endpoints, a byte for the width, 3 bytes for the color etc. So tens of bytes.
Your scan is a raster image, which is a line-by-line full storage of the scene without regard for whether any particular region is of any value to the reconstruction of the scene (i.e. blank white paper is treated the same as a line). So a simple line in a white square needs to be broken up into an arbitrary grid and each and every grid cell needs to be stored. A postage stamp at 300dpi is several hundred bytes.
For an RGB 8-bit raster image, the scene is stored as 3 b&w images called "channels" with 1 byte per pixel per channel.
I am guessing you are scanning the drawing in color at full size and choosing 300dpi, since (300x11) x (300x17) x 3 / 1024 / 1024= about 50MB.
You can reduce the size of your scan by a factor of 3 by converting to greyscale. JPeg or PNG compression may also be suitable. If the content can handle lower resolution without losing meaning (i.e. back of envelope sketch or modification to a booth/room layout etc), then try reducing the scanning dpi (try 240 or 120 etc).
If you are talking about drafting/cad style imagery, you might benefit from doing a "live trace" on the scanned image using vector-oriented software. Remember to delete the raster object after the trace or it might still be included in the file.