1.We can get the maximum of net product from the following function:Y=13X-X^2-X,the X must be 6;
2.Assuming there are X1 children raised by the first resident, then we can maximize the net product of the first resident:Y=13X1-X1(X1+X2)-X1,the result is that X1=6-(X2 / 2);
3.This question is inclined to check the nash equilibrium,which is a fundamental notion of game theory.The nash equlibrium in this question is X1=6-(X2 / 2), X2=6-(X1/2), easily, we can get the answer:x1=x2=4