$U(x,y) = x + 4y$, I tried to find demand function for good x, so I did utility maximization.
max $U(x,y) = x + 4y $ subjects to $P_x.x + P_y . y = I$
and I found the $Px /Py = 1/4$, so $4Px = Py$.
Plug it in budget constraint I found $P_x.x+4P_x.y = I$
My Question is when I write demand function for good x, should it be $x = I/P_x$ because I said $y = 0$
So, Can I say that there is corner solution?