1.
x+y+z
xyz=125
x+y+z=lambda(xyz-125)
x+y+z-lambda(xyz-125)=F(x,y,z,lambda)
x+y+z-lambdaxyz-lambda125
F_x=1-lambdayz=0
F_y=1-lambdaxz=0
F_z=1-lambdaxy=0
F_lambda=xyz-125=0
lambda=75
x=1,y=7
z=25
x+y+z=33

2.
x+y+z=15
xyz
xyz=lambda(x+y+z-15)=F(x,y,z,lambda)
xyz-lambda(x+y+z-15)
F_x=yz-lambda
F_y=xz-lambda
F_z=xy-lambda
F_lambda=x+y+z-15
x=6,y=3,z=6
xyz=108