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Math Help - Optimization Problem

  1. #1
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    Unhappy Optimization Problem

    If 1700 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
    Volume = cubic centimeters

    1700 = x^2+4*x*h
    4xh=1700-x^2
    h=1700-x^2/4x
    V=x*(1700-x^2/4)
    =1700x-x^3/4
    V(x)=1700/4x-1/4x^3
    V'(x)=1700/4-3/4x^2
    set v'(x)=0
    1700/4-3/4x^2=0
    3/4x^2=1700/4
    3x^2=1700

    I am really stuck and i need some guidence and some to compare their answers with me.
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  2. #2
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    Quote Originally Posted by jpratt View Post
    If 1700 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
    Volume = cubic centimeters

    1700 = x^2+4*x*h
    4xh=1700-x^2
    h=1700-x^2/4x
    V=x*(1700-x^2/4)
    =1700x-x^3/4
    V(x)=1700/4x-1/4x^3
    V'(x)=1700/4-3/4x^2
    set v'(x)=0
    1700/4-3/4x^2=0
    3/4x^2=1700/4
    3x^2=1700

    I am really stuck and i need some guidence and some to compare their answers with me.

    \displaystyle V = 425x - \frac{x^3}{4}<br />

    \displaystyle V' = 425 - \frac{3x^2}{4} = 0

    \displaystyle x = \sqrt{\frac{1700}{3}}

    this value of x yields a maximum since v'' < 0 for all values of x in the usable domain.
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