5. Suppose that, for a certain consumer, whenever the price of $x$ is twice the price of $y$ (ie, $P_x = 2p_y$), the consumer optimally consumes twice as much $y$ as $x$ (ie, $y = 2x^*$). Which of the following utility functions represent preferences consistent with this behavior?
(a) $U(x, y) = 2\ln(x) + y$
(b) $U(x, y) = 3x + y$
(c) $U(x, y) = \min\{4x, 5y\}$
(d) $U(x, y) = \ln(x) + 2\ln(y)$
(e) $U(x, y) = xy$
