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 mistakes). 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) Lagrange function for obtaining extreme values of z=xy under linear constraints 2x=y

Formulate as and describe the first condition and obtain the stop values. Obtain the conditions of the second order using the Euterheian and check for maximum or minimal.