At consumption levels (x, y) of two good, a consumer draws total utility given by the function u(x, y) = x0.5y0.3 The prices are Px = $2, P = $6, and the consumer has allocated $384 to the consumption of the two goods. (i) Specify the Lagrange function for utility maximization subject to budget constraint. (ii) Specify and solve the equations of the 1st-order conditions for (,, ).