Hi. I am trying to maximize the function F(x,y,z)=xyz, under the constraint 2x +2y+z=84, with theta being represented by m.

Derivatives:

Fx= yz+2m=0

Fy= xz+2m=0

Fz= xy+m=0

Fm= 2x+2y+z-84=0.

I found m= -yz/2, and m= -xz/2, getting y=x. I proceeded to find z= -2y.

I then plugged everything into Fm and got y=42. What am I doing wrong, as the correct answer should be (14,14,28)?

Many thanks