Will grass carp control water primrose if it is the only major vegetation in a pond? I want to keep it closer to shore since it is along 2/3rds of the shoreline, not eliminate it. It is tough fishing when it extends 5-6' from the accessible shore. The steep, inaccessible brushy shore does not have it. How many would I need for a triangular shaped 3 acre pond?

See this link. Goats will eat it. We control (not eradicate) ours by pulling it out with rakes over the summer. If it gets to bad you can use the other methods in the link.

http://aquaplant.tamu.edu/database/emergent_plants/water_primrose_mgmt.htm

Goats will not work, they usually eat everything but the intended victim. My property is also a woodlot with lots of nice tender baby oak and hickory sapling, not to mention all of the acorns and hickory nuts from their parents. Now, the rake sounds simple and cheap, they also will not die. I had a bad experience on a deer lease with 1200 dead and dieing goats when angora subsidies went away. The grazing lease specified no more than 400 goats. I don't really like them anymore.

jeffreythree, goats work very well, they will "manicure" your ponds in a way not humanly possible.
As you mention they have to be managed as any livestock, or pond fish...

My son rotates his goat herd beteween pastures - some wooded with browse, other with pasture grasses.
Great animals, and as ewest says, "they love water primrose.

ps: the "bare spots" in the photo occured during the record drought years - not from overgrazing.

Grass carp will eat water primrose, IF that is all they have to eat.
They will become "feed trained"...

Goats don't work for me ... and I there is nothing else for them to eat!

You guys may have different goat breeds which could account for different diets.