Please answer all parts.

2. Consider the following problem: Minimize x} + 2x subject to - X1 +650. a. Write the KKT necessary conditions. b. Find a KKT point (x1, x2) and the Lagrange multiplier u associated with the constraint. C. Formulate the auxiliary function F(x1, x2) using the Barrier function B(x) = - In(-9(x)) and the barrier parameter u > 0. d. Is F(X1, X2) strictly convex? e. Analytically solve VF(x1, x2) = 0. (Recall that it must be in the interior of the feasible region.) f. For what range of values of u, the solution in (e) is within the distance of 0.01 from the solution in (b)? =