math

A farmer has 25 yards of fencing to make a pig pen. He is going to use the side of the barn as one of the sides of the fence, so he only needs to fence 3 sides. What should be the dimensions of the fence in order to maximize the area?

  1. length of side parallel to barn ---- y
    length of each of the other two sides --- x
    y + 2x = 25
    y = 25-2x

    area = xy = x(25-2x) = -2x^2 + 25x

    d(area)/dx = -4x + 25 = 0 for a max of area
    4x = 25
    x = 25/4 , then y = 25 - 25/4 = 25/4
    state your conclusion

    or

    from :
    area = -2x^2 + 25x , a downwards parabola,
    the x of the vertex = -b/(2a) = -25/-4 = 25/4 , as above
    y = ...... , same result

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