若x+y+z=30,3x+y-z=50,x,y,z都为非负实数,则M=5x+4y+2z的取值范围是_.

问题描述:

若x+y+z=30,3x+y-z=50,x,y,z都为非负实数,则M=5x+4y+2z的取值范围是______.

由题意得x+y+z=30     ①3x+y−z=50    ②,且x≥0,y≥0,z≥0由②-①得   x-z=10,即x=10+z由①×3-②得   2y+4z=40,即y=20-2z,又∵x≥0,...