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A farmer has 1000ft of fence and wishes to enclose the largest possible area that has four individual square pens bordered by a rectangular pen of a different width on each end. what are the overall dimensions of the fence area with maximum square footage?

so far i thought i could set up the area equation to be A= 4(x^2) + 4xy and then take the derivative but im not getting the correct answer

  • math -

    what is the Tenths place

  • math -

    what is the tenths place?

  • math -

    IN the fraction 4.5, the five is in the tenths place.

    For matt: I don't understand how a rectangular pen can have a different width n each end.

  • math -

    yeah i don't understand the wording but the diagram shows that each end of the entire rectangular pen is 2x

  • math -

    I could be a matter of interpretation.
    It said, "four individual square pens bordered by a rectangular pen of a different width on each end"
    You have the rectangles fanning out on one side of the squares. Could it not also mean that they fan out on all sides of the squares, so that there would be 10 rectangles with the squares in the middle?
    Just wondering if that is the problem.

    Anyway, according you your interpretation, I got
    20x + 5y = 100
    4x + y = 25
    y = 25-4x
    for
    A = 4x^2 + 5x(25-4x)
    expanding this, differentiating and setting that equal to zero, gave me
    x = 25/6 ft.

    If you also got that, try the different interpretation.

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