somewhere here there's a current discussion of the feasibility of raising meat bird through the summer months without supplying feed. Centrarchid has some experience and is involved in that discussion, so you could maybe find it through searching for those posts.
The birds they are talking about are game type, old type, not big meaty birds like cornish x or the pure Cornish that I keep for meat.
From my own experiences, I do not believe it is possible for the home grower to equal or beat the supermarket price on chicken. As has been said, we do it so we know what we are eating, also in my opinion the quality of the meat is much better. No tasteless mushy meat pressure impregnated with "15% broth" and whatever chemicals are in that.
I had a restaurant ask me if I would raise pastured heritage breed meat chickens for them, and I showed them a breakdown of the costs. So I'll toss out some of the numbers from that, which shows a best possible sort of scenario in my area in my conditions.
Cheapest Dark Cornish rooster chicks I found were $2.80 each, plus $19 to ship 25-35.
A purebred eats about 8 lbs. of feed for each lb. growth
With free ranging, figure about 13 weeks to slaughter weight.
My local feed runs about $13 per 50 lbs. (don't forget your gas cost to go get this)
Are you going to butcher them yourself? I do sometimes but I don't have a plucker, and then I skin them, which not everybody likes. If I take them to a poultry processor the cheapest I can get to is $2.80 per bird. The ones close to me charge $4 and $5 per bird. Don't forget your gas costs to transport them.
Any way, in the best possible world, for 20 chickens, it came to something like $7-8 direct out of pocket cost per bird, for some very nice meat birds weighing 3 to 4 lbs each.
I hope this is helpful.