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You make a profit by selling the eggs for more than your expenses, which would be a certain percentage of your gross regardless of the number of hens. 
The number of hens doesn't have a lot to do with it, except that there are economies of scale, if you have a large number of birds you can buy feed in bulk at a cheaper cost and housing costs might be slightly cheaper.
Let's say you are raising your own chicks, feed is $15 for 50 lbs, and (for the sake of this exercise) you expect hens to be replaced after one year of laying.
Chick:                         $2
Feed to 18 weeks:     $5
Chick cost per dozen (for 24 dozen salable eggs in one year)   $0.30
Feed per dozen (.25 lbs per day for 14 days)                            $1.05
Plus any repairs, utilities, consumables you use:                       $0.25 ??
Coop and equipment costs don't really figure into expenses as they are assets.  If you keep them in general repair they are generally worth what you paid for them and they could possibly be sold for that much.
So by my numbers, expenses are $1.60 per dozen.  Selling at $2/dz you net $0.40.  At $3.00 per dozen you net $1.40.
You can make a profit with one hen...  At $3.00 a dozen there would be a profit of $34 over the course of a year with one hen.