Constrained Optimization: More variables, more constraints

Consider the following problem: 0 Minimize f(:1:, y, z) = 51:2 + y2 -| 22 22 | 1, 0 Subject to the constraints a: + y -| z = 2 and 2st + y 22 = 4. (a) Write the Lagrangian for this problem. (b) Write the system Whose solutions are the critical points of f (2:, y, 3). Find these point(s). (c) Write the bordered Hessian that must be tested. Use it to determine Whether the critical point (s) give you a local minimum or maximum. Explain all your work