1.
x^3+x^2z+y^2z-xyz+y^3
=x^3+y^3+x^2z+y^2z-xyz
=(x+y)(x^2-xy+y^2)+z(x^2-xy+y^2)
=(x+y+z)(x^2-xy+y^2)
=0
2.
3y+2z=3+x(1)
3y+z=4-3x(2)
(1)-(2)：z=4x-1
代入(2)：
3y+4x-1=4-3x
y=(5-7x)/3
x≥0
z=4x-1≥0
y=(5-7x)/3≥0
解得1/4≤x≤5/7
M=3x-2y+z
=3x-2*(5-7x)/3+4x-1
=(35x-13)/3
(35*1/4-13)/3≤(35x-13)/3≤(35*5/7-13)/3
-17/12≤M≤4