algebra

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a local grocery store has plans to construct a rectangular parking lot that is bordered on one side by a highway. there are 1280 feet of fencing avaliable to enclose the other three sides. find the dimensions that will maximize the area of the parking lot.

  • algebra -

    Let the length be y ft and the width be x ft.
    (I am looking at 2 widths and 1 length)

    so y + 2x = 1280
    y = 1280-2x

    Area = xy
    = x(1280-2x)
    = - 2x^2 + 1280x

    complete the square ....

    Area = - 2(x^2 - 640x + 102400 - 102400)
    = - (x - 320)^2 + 204800

    so x = 320 , then y = 1280-640 = 640

    the width is 320 ft, and the length is 640 ft

  • algebra -

    3rd last line should say

    = -2(x - 320)^2 + 204800

    typo at the -2 in front, does not affect the answer.

  • algebra -

    dimensions: 320x640
    max. area 204800

  • algebra -

    ergjoiso;gs;g

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