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Math Help - Optimization-Open Topped Cylinder

  1. #1
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    Optimization-Open Topped Cylinder

    This question is really bothering me help would be much appreciated

    The cost per square meter of the sides of an open-topped cylindrical tank is twice the cost per square meter of the bottom. Find the most economical proportions for a tank of given volume.
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    Quote Originally Posted by Calculus23 View Post
    This question is really bothering me help would be much appreciated

    The cost per square meter of the sides of an open-topped cylindrical tank is twice the cost per square meter of the bottom. Find the most economical proportions for a tank of given volume.
    V = \pi r^2 h

    h = \frac{V}{\pi r^2}


    C = \pi r^2 + 2(2\pi r h)

    sub in the expression for h in terms of r in the cost equation to get C as a function of r, simplify, and find dC/dr to find the minimum cost.

    remember that V is just a constant.
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    I am still confused... any more help?
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    Quote Originally Posted by Calculus23 View Post
    I am still confused... any more help?
    I've told you exactly what to do.

    1. substitute \frac{V}{\pi r^2} in for h in the cost equation.

    2. simplify the cost equation.

    3. take the derivative of the cost equation w/r to r and minimize like you were taught in class.
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