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______.
答
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,...