若x+y+z=30,3x+y-z=50,x,y,z均为非负数,且m=5x+4y+2z,试求m的最大值与最小值.

x+y+z=30 (1)
3x+y-z=50 (2)
5x+4y+2z=m (3)
(1)+(2)
4x+2y=80
2x+y=40 (4)
(2)*2+(3)
6x+2y+5x+4y=100+m
11x+6y=100+m (5)
(4)*6-(5)
12x+6y-11x-6y=240-100-m
x=140-m
y=40-2x=2m-240
z=30-x-y=130-m
因为x,y,z均为非负数
所以x>=0,y>=0,z>=0
140-m>=0,m=0,m>=120
130-m>=0,m