$$ x+2y+3z = 15 $$
Find the maximum value of $$ 6(1+x)yz + x(2y+3z) $$
I substituted $2y+3z=15-x$ And tried to use AM GM to find maximum value of $xyz$ but they don't occur at same value. I know that this is not the right way to do it but I don't have any idea on how to do these type of questions.
How do I proceed?
Do note that $x,y,z$ are positive real numbers.