Find the maximum value of log(x) + log(y) + 3log(z) on the octant of the sphere x^2 + y^2 + z^2 = r^2.

Deduce that if a,b and c are real numebrs, abc^3<=27[(a+b+c)/(5)]^5

I've done the first part (I think). Not suire at all about the second though.. I guess it uses Lagrange multipliers but cant see what to you as the constraints etc

many thanks