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Math Help - optimization problem

  1. #1
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    optimization problem

    question:
    find the length and width of a rectangle that has the given perimter and a maximum area

    data given:
    perimeter = 80meters

    --------------------------------------

    any help?
    2l+2w=80 <--- put in terms of either variable???

    i got [80-2w/2] = Length

    and i plugged this into the equation for the area of a rectangle...

    Area = L*W
    -----------------------
    area = [80-2w/2] * W

    then i differentiate area = [80-2w/2] * W and find the critical numbers and get the maximum.....am i doing this correct lol?
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  2. #2
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    Quote Originally Posted by nuclear123 View Post

    area = [(80-2w)/2] * W

    yes ... it might make things easier if you simplify as you go along.

    A = (40-w)w
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