JNU SSS 2016 Question 35: Budget constraint and consumer equilibrium

Let the following utility function represent the preference relation of an individual : $U(x,\ y) = x^{1/2} + y$ Let $P_x$, $P_y$, $M$ denote the prices of goods $x$, $y$ and money income respectively; $P_x$, $P_y$, $M > 0$.

Let $P_y = 2,\ P_x = \frac{1}{4M}$ Optimal consumption bundle includes