p(x,y)满足3x-y-60b>0)最大值为12则2/a+3/b的最小值为多少?
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![p(x,y)满足3x-y-60b>0)最大值为12则2/a+3/b的最小值为多少?](/uploads/image/z/6935275-19-5.jpg?t=p%28x%2Cy%29%E6%BB%A1%E8%B6%B33x-y-60b%3E0%29%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%BA12%E5%88%992%2Fa%2B3%2Fb%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BA%E5%A4%9A%E5%B0%91%3F)
p(x,y)满足3x-y-60b>0)最大值为12则2/a+3/b的最小值为多少?
p(x,y)满足3x-y-60b>0)最大值为12则2/a+3/b的最小值为多少?
p(x,y)满足3x-y-60b>0)最大值为12则2/a+3/b的最小值为多少?
将Z=ax+by化为:y=z/b-a/b*x.
建立平面直角坐标系,将3x-y-6<=0,x-y+2>=0,X>=0,Y>=0画出,即线性规划.
由于a>0,b>0,故-a/b<0.可知p(4,6){(4,6)为3x-y-6=0与x-y+2=0交点}有12=4a+6b,之后用乘“1”变换:即1=a/3+b/2,故(a/3+b/2)*(2/a+3/b)=(2/a+3/b).
对于(a/3+b/2)*(2/a+3/b),化简:2/3+3/2+a/b+b/a>=13/6+2=25/6(当且仅当a=b=1时有最小值.).
故2/a+3/b最小值为25/6.