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sue has 100 ft of fencing she wants to put around a rectangular area next to her barn the barn will form one side of that area. Find the dimension that will enclose the maximum area. Find the maximum area 

Guest Nov 27, 2018
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Let x be the number of feet of fence on each side of the area  perpendicular to the barn

 

So......the side parallel to the barn is (100 - 2x)

 

So....the area, A  =   x(100 - 2x)  

 

A = -2x^2 + 100x

 

This will be a parabola turning downward

 

The x coordinate that maximizes the area is given by the x coordinate of the vertex =

 

-100 / [ 2 * -2] =   -100 / -4   =   25 ft  = x

 

So....the dimensions are     (25) (100 - 25) = 25 ft x  75 ft

 

And the max area is    25 * 75   =  1875 ft^2

 

 

cool cool cool

CPhill  Nov 27, 2018

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