Using the Kuhn-Tucker theorem32 find an optimal solution to a consumption utility maximization problem with an additional constraint on the supply of both

goods: 0x bi, i = 1, 2, when a utility function is: (a) a power function: u(x) = = axx2, a, ai > 0, a + a < 1, i = 1, 2, (b) logarithmic: u(x) = a ln x + a2 ln x2, ai > 0, xi > 0, i = 1, 2, (c) subadditive: u(x) = ax + ax2, a > 0, i = 1, 2, a (0; 1).