6. (10 points) (a) (3 points) Given 2 = 27(y + 4) subject to I + y = 8. Use the Lagrange multiplier method to nd the local optimum value of z, as well as the optimal I and 3;. Is the above solution a minimum or a maximum? (b) (7 points) Use the Lagrange Multiplier method to prove that a triangle with maxi- mum area that has a given perimeter of 2 must be equilateral. Can the solution be found using the Lagrange method