III. Once again, suppose that a consumer's utility function is given by u (x1, x2) = kx1 + 22, where k represents a positive constant. Prices are P1 = 1, P2 = 2. Suppose that we are interested in finding the minimum amount of income needed to achieve a utility-target > 0. a) Specify the Lagrangean using the minimum-utility constraint and the non-negativity constraints on xi and x2. b) Using the Lagrangean, determine the range of values for such that the constraint a > 0 binds. c) Determine the possible values of the Lagrange multiplier 11 attached to the minimum-utility constraint in the two cases when the constraint x1 > 0 binds and when it does not bind. III. Once again, suppose that a consumer's utility function is given by u (x1, x2) = kx1 + 22, where k represents a positive constant. Prices are P1 = 1, P2 = 2. Suppose that we are interested in finding the minimum amount of income needed to achieve a utility-target > 0. a) Specify the Lagrangean using the minimum-utility constraint and the non-negativity constraints on xi and x2. b) Using the Lagrangean, determine the range of values for such that the constraint a > 0 binds. c) Determine the possible values of the Lagrange multiplier 11 attached to the minimum-utility constraint in the two cases when the constraint x1 > 0 binds and when it does not bind