The maximization problm does not hav a solution by he following arguements
the domain is given to be an open set x belongs to (0,1)....consider a value x=x1 such that it belongs to (0,1) and very close to 1, now there exists an epsillon>0 such that x1+epsillon also belongs to the set (0,1)
the function is strictly increasing in x so higher the value of x higher will be te value of the function x^2
x1^2 < (x1+epsillon)^2
so no solution
Akshay Jain
Masters in Economics
Delhi School of Economics
2013-15