作业帮哥哥姐姐 A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle.How can he do this so as to minimize the cost of the fence?(Give the
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哥哥姐姐 A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle.How can he do this so as to minimize the cost of the fence?(Give the
哥哥姐姐
A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle.How can he do this so as to minimize the cost of the fence?(Give the dimensions in increasing order.)
哥哥姐姐 A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle.How can he do this so as to minimize the cost of the fence?(Give the
比如你的field的长是x,宽是y,则你需要的总长度是2x+3y,或者是3x+2y,比如你的cost是a,则你需要考虑的是让(2x+3y)a最小或者(3x+2y)a最小,其实就是让2x+3y最小或者让3x+2y最小
根据均值不等式,3x+2y≥2√6xy=2√9×10^6=6×10^3,所以当3x=2y时,花费最小
同理,如果是2x+3y,最小值也是6×10^3,即2x=3y的时候,花费最小
综上：如果你的field的长宽比例是3：2,(即长1500feet,宽1000feet),且中间那块儿fence的长度跟宽一样长,即1000feet,那么花费最小,或者是,如果你的field长宽比例是2：3,(即长1000feet,宽1500feet),且中间那块儿fence的长度跟长一样长,即1000feet,那么花费最小
it's just a simple math in CN.
一个农夫想围栏面积1.5万多平方英尺,然后在一个长方形的领域划分它用一个围墙在平行于一半的其中一个边矩形。他怎么能这么以成本最小的栅栏吗?(给的维度上增加订单。)