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A rectangular cow pasture is enclosed on three sides by a fence and the fourth side is part of the side of a barn that is 400 feet long. The fence costs \$5 per foot and \$1200 altogether. To the nearest foot, find the length of the side parallel to the barn that will maximize the area of the pasture.

Jan 26, 2019

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A rectangular cow pasture is enclosed on three sides by a fence and the fourth side is part of the side of a barn that is 400 feet long. The fence costs \$5 per foot and \$1200 altogether. To the nearest foot, find the length of the side parallel to the barn that will maximize the area of the pasture.

Dividing  1200 by 5 tells us how many feet of fencing we can afford.....so  ....1200 / 5 = 240 ft

Let the side of the fence paralleling the barn be x feet

Then....one of the other sides  perpendicular to the barn can be represented as   (240 - x) / 2

So....the area to maximize is

A =  x (240 - x) / 2       simplify

A = (240x - x^2)/ 2

A = (-1/2)x^2 + 120x

The x  that will maximize this is given by :      -(120) / (  2 * (-1/2) )  =  120 ft

And this is the length of the fence parallel to the barn that will max the area

Jan 26, 2019