*********************Please make sure both part a and b are solved*************************

a) Solve the following problem using Lagrange multiplier method and find the optimal value of f(X). Maximize f(X) = x2 + y2 + 2? subject to the constraints: g(x): 0.25x2 + 0.2y2 + 0.047 = 1 g2(X): x+y-z=0 b) If the constraint, g2(X), is now changed to: g2(X): x+y-0.97z= 0, using sensitivity analysis, determine a (new) approximate optimal value of f(x). a) Solve the following problem using Lagrange multiplier method and find the optimal value of f(X). Maximize f(X) = x2 + y2 + 2? subject to the constraints: g(x): 0.25x2 + 0.2y2 + 0.047 = 1 g2(X): x+y-z=0 b) If the constraint, g2(X), is now changed to: g2(X): x+y-0.97z= 0, using sensitivity analysis, determine a (new) approximate optimal value of f(x)