Find the quantities of each product that the consumer should buy, subject to the budget, that will allow maximum satisfaction. That is, find values of x and y that maximize $U = f(x, y)$, subject to $xp_x + yp_y = I$. Assume that such a maximum exists.
$U = x^2y$; $p_x = 7$, $p_y = 3$, $I = 168$ ($x^2y \neq 0$)
The values that maximize U are x = $oxed{}$ and y = $oxed{}$
(Simplify your answers.)