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A box must have base x cm by 2x cm. what are the dimensions of the box of maximum volume if its length+width+depth<140cm

  • math -

    2 x^2 h = v
    h = 140-3x

    v =2 x^2 (140-3x)
    v = 280 x^2 - 6 x^3
    dv/dx = 0 = 560 x - 18 x^2
    x(560 - 18x) = 0
    18 x = 560
    x = 31.1

    2x = 62.2

    h = 140 - 3(31.1) = 46.7

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