2006 MDX tire issue

I have a 2006 MDX. I just ran over a sharp piece of metal that logged itself
in one of my rear tires. Of course it created a flat. My question is does
anyone know the parameters for using a plug (or patch)? The tire has about
3000 miles on it and other than a small gash in the center of the tread it's
fine. The total length of the cut is about 3/4 to 1 inch. A new tire is
about $180. If it's a safety issue I have no problem buying a new tire.
However if a plug will be just as good I rather not spend the $$$.

Thanks in advance.

John