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

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 06:02:17
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
xQMN@ C)5.n~jmDjFK\iڴ R >@Du3|~fY@E&.$D?y$\cz=E =*Lf;vvyɖYv5[=ݦ}v*$zAES?PwTLTJbI8ᱛ!?S R7(Q+=P" iazuvQ X,Z8Zh5*?e{m/ձ(h%Y^dpʡVb~yq~ӭY0}k{W/&

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