The problem is to choose x to maximize f(x;a) = ax- 3x^2, where á is exogenous, subject to the constraint

x>0and x=0.

(a) For this problem, which values of x are on the boundary, and which are in the interior?

(b) Calculate the first-order condition for this problem.

(c) If a=12, then which value of x solves the problem? Justify your answer carefully.

(d) If a=!2, then which value of x solves the problem? Justify your answer carefully. What is the maximized value of f?

(e) For which possible values of á does this problem have a solution on the boundary?