For the next two parts, consider the function f(x) =2 and the constrained program min f(x) subject to x e [0,3] (a) Show that the optimal solution to the centering step for the log-barrier method is 1 by solving min f(x) - log(x)-log(3-) and assuming log(v) = oo when y 0. (b) Using the optimal centering initialization, compute (by hand and showing your work) roter and rter from the log-barrier method using 2 inner backtracking iterations with steepest descent increments for f(x) = with = = 1/2. This means that you will compute 4 backtracking steps by hand. Use M = 2 so that router is a numerical approximation to the solution of min f()- log-log(3-) and then a2) is a numerical approximation to the solution of min f()- ^log)-log(3-) You may use the Python implementations of the log-barrier method and backtracking to check your work and that inequalities hold, but your answers should be exact