Hmmm...
SO... She is selling these super valuable eggs for profit, and then paying the orphanage for the child labour with those profits.
But she wants to raise production to cheapen the eggs so anyone can buy them.
Fine for the buyers, but doesn't that mean the kids will have to do 10 times the work for the same pay? Or is she making enough money to employ 10x as many orphans? In which case where exactly is she going to get 10x as many orphans from? Is she planning on going around killing parents so she can get more workers for her poultry farm? Or perhaps lowering the workload by factory-farming with the birds in tiny cages?
OR is she going to get some male cluckers and engage in selective poultry-breeding to maximise egg yield over generations?