x+y+z=1,x大于等于0且小于等于1，y大于等于0且小于等于1，2y+z大于等于3／2，求M=2x+5y+4z的最大与最小值 高中数学必修五题目。已知x，y满足条件:x-y+1大于等于0...
x-y+1\u5927\u4e8e\u7b49\u4e8e0,x+y-2\u5927\u4e8e\u7b49\u4e8e0,x\u5c0f\u4e8e\u7b49\u4e8e1,\u6c42z=\uff08x+2y)/(2x+y)\u7684\u8303\u56f4\u89e3\uff1a\u7531\u610f\u4e49\uff0c\u753b\u51fa\u7ebf\u6027\u89c4\u5212\u56fe\uff0c\u53ef\u4ee5\u770b\u51fa\u6ee1\u8db3\u6761\u4ef6\u7684\u89e3x>0\uff0cy>0.
\u5219z=\uff08x+2y)/(2x+y)=[(x+y/2)+3y/2]/(2x+y)=1/2+3y/(4x+2y)=1/2+3/(4x/y+2).
\u5176\u4e2dx/y\u53ef\u4ee5\u770b\u6210\u70b9(x\uff0cy)\u4e0e\u70b9(0\uff0c0)\u8fde\u6210\u7684\u76f4\u7ebf\u7684\u659c\u7387\u7684\u5012\u6570.
\u7531\u56fe\u53ef\u77e5\uff1a\u5f53x=1/2\uff0cy=3/2\u65f6\uff0cx/y\u53d6\u5f97\u6700\u5c0f\u503c1/3\uff1b
\u5f53x=1\uff0cy=1\u65f6\uff0cx/y\u53d6\u5f97\u6700\u5927\u503c1.
\u52191/3\u2264x/y\u22641\uff0c4/3\u22644x/y\u22644\uff0c10/3\u2264(4x/y+2)\u22646\uff0c1/2\u22643/(4x/y+2)\u22649/10.
\u56e0\u6b641\u2264z=1/2+3/(4x/y+2)\u22647/5.
\u6536
由x+y+z=1,z=1-x-y,M=-2x+y+4,y=2x+M-4；
又由0≤x≤1，0≤y≤1，y≥x+1/2 ，得x、y只能在如图（7）所示的阴影区域内变化，
而M－4为直线在y轴上截距，随着M的变动，形成了一系列平行直线，M-4在0到1之间变化，
所以4≤M≤5，
M的最小值是4，最大值是5
M的最小值是4，最大值是5
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