若X+Y+Z=30,3X+Y-Z=50,X、Y皆为非负数,求M=5X+4Y+2Z的取值范围

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若X+Y+Z=30,3X+Y-Z=50,X、Y皆为非负数,求M=5X+4Y+2Z的取值范围
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若X+Y+Z=30,3X+Y-Z=50,X、Y皆为非负数,求M=5X+4Y+2Z的取值范围
若X+Y+Z=30,3X+Y-Z=50,X、Y皆为非负数,求M=5X+4Y+2Z的取值范围

若X+Y+Z=30,3X+Y-Z=50,X、Y皆为非负数,求M=5X+4Y+2Z的取值范围
由题意,Z=30-X-Y,
代入M=5X+4Y+2Z,有
M=5X+4Y+2(30-X-Y)=3X+2Y+60
X+Y+Z=30,3X+Y-Z=50,两式相加得:4X+2Y=80,化简2X+Y=40
有X=(40-Y)/2,Y=40-2X
将X=(40-Y)/2代入M=3X+2Y+60,有M=120+Y/2,即Y=2(M-120)
将Y=40-2X代入M=3X+2Y+60,有M=140-X,即X=140-M
因为X、Y为非负数,所以Y=2(M-120)大于等于0,X=140-M大于等于0
综合有,140大于等于M大于等于120