Consider the problem min f(x) = - $7 - 312 s. t. $2 = 0. (a) Calculate the optimal solution and the Lagrange multiplier. (b) For k = 0, 1, 2 and * = 10*+ calculate and compare the iterates of the quadratic penalty method with 1* = 0 for all k and the method of multipliers with A" = 0. (c) Suppose that c is taken to be constant in the method of multipliers. For what values of c would the augmented Lagrangian have a minimum and for what values of c would the method converge