(1) The utility indicators that a consumer A obtains from two goods X and Y appear as functions u(x,y)=x^2y^3 (x and y represent the consumption of two goods and are nonnegative real number). Formulate the utility maximization problem under A's budget constraint using the Lagrange function when A's budget is 300,000 won and X and Y's prices are 20,000 won and 10,000 won, respectively. Find and explain the consumption of both goods using the first and second-tier conditions for the maximization problem. Find and explain what the marginal utility of income is.

(2) Formulate the problem of obtaining polar values of z=xy under linear constraints 2x+y=2 as a Lagrange function, describe the first coefficient, and obtain the stationary values. Obtain the conditions of the second order using the Boderd Hessian and check for maximum or minimal.

(1) A X Y u(x,y)=x^2y^3 . ( x y .) A 30, X Y 2, 1 A . 1 2 . . (2) 2x+y=2 z=xy 1 . 2