Let x, y, z be real numbers such that x + y + z = 1, and x >= -1/3, y >= -1, and z >= -5/3. Find the maximum value of sqrt{3x + 1} + sqrt{3y + 3} + sqrt{3z + 5}.
The maximum value is sqrt(8) = 2*sqrt(2), for x = 0, y = 0, and z = 1.
+101 
