A consumer's utility function is given as , the price of and goods is and , and the income is given as . () (1) Find the first and second sufficient conditions for maximizing utility. (2) Find the properties that the function should satisfy as a sufficient condition for the maximum to be maximized at the same time. (3) Find the demand functions and and explain their features.

ux, y) = v(2) + y = 2 P. Py 0