A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals. What dimensions should be used so that the enclosed area will be a maximum?

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amarantha41 · Accepted Answer

To get the dimensions of our rectangle, we must first determine x and y.We can see from the sketch that we have2x+3y=400⇒x=200−32yOur area isA(x,y)=2xyAs we can see from the first equation, our function isA(x,y)=2xyWe can see from the first equation that we have So our function isA(x,y)=2xyA(y)=2⋅(200−32y)⋅yA(y)=(400−3y)y⇒A(y)=−3y2+400yThe first step is to identify critical numbers and solve them -A′(y)=0This leads to&amp;nbsp;A′(y)=−6y+400So our equation becomes−6y+400=0⇒y=2003When we plug this into expression for x, we getx=200−32y⇒x=100As a result, our ultimate dimensions arex=100;y=2003

A rancher has 400 feet of fencing with which to

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