Problem 1. Using the Lagrange method, solve the following constrained optimization problems. In order to get full credit, you may choose to manipulate the objective, but you are not allowed to substitute in the constraint: you must use the Lagrange method. Please check for the rst order and local second-order sufcient conditions. (a) (15 points) Minimize f(:c,y) = 3:2 + y2 subject to :1: + cy = 1, for (1:, y) E R2, where C is an an arbitrary real-valued constant. (b) (15 points) Minimize f(:n,y) = :1: + :9, subject to $2 + y2 = 1, for (m, y) E R2