Consider the following minimization problem: f(x, y, z): 22. + y + z - xy - xz+yz + x-3y - 2z + 4 = (a) Find the global minimizer and the optimal objective functional value analytically. (b) Alternatively, we consider the numerical approach. With an initial guess of [x0), y(0), 2(0)] = [0,0,0], perform one iteration of the steepest de- scent algorithm. Show all the computational steps. (c) With an initial guess of [x0), y, z(0)] = [a, b, c] (where a, b, c are the last three digits of your student ID number), perform one iteration of the Newton's method. Show all the computational steps.