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Math Help - Optimization problem - setting up equations

  1. #1
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    Optimization problem - setting up equations

    A large soup can is designed to be so taht the can will hold 16pi cubic inches of soup. Find the values of x and h for which the amount of metal needed is as small and possible


    x = radius of the cylinder
    h = height of the cylinder

    I'm having trouble setting up the objective and constraint equations

    Obviously, objective is the entire surface area of the cylinder, so:
    Area = 2*pi*x^2 + 2*pi*x*h

    But for the constraint equation, i can't figure out how to only write it with one variable because you need both in the volume equation which is what they give you 16pi for

    vol = 16*pi = pi * x^2 * h

    Basically, how can I set these equations up so I can solve them? Thanks!
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  2. #2
    Junior Member
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    Nov 2009
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    Re: Optimization problem - setting up equations

    From the volume equation you have h = 16/x^2. Then you can substitute out h in the area expression and you will be left with a single variable optimization problem (that variable being x).
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