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Math Help - Finding Applied Minimum of a Poster (Calculus Word Problem)

  1. #1
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    Finding Applied Minimum of a Poster (Calculus Word Problem)

    I've been doing pretty good on these Min/Max problems so far, but this one is kind of getting to me. It goes like this:

    Determine the minimum area of a poster that will contain 50 square inches of printed material and have 4 inch margins on the top and bottom and 2 inch margins on the left and right. Prove your answer.
    I was able to draw out a rectangles and define the x and y sides while filling in the appropriate labels. It looks like this:



    It's very messy, and I apologize for that, but it's the best I could do and it fits the description I gave. How do I go about setting this one up so I can find the derivative, factor it, get the points (min and max), and find the restrictions?


    EDIT: And also, this one is kind of stupid, but I'm pretty burnt out and I just can't factor this problem for some reason.

    12x^2 - 36x^3

    Once I get that, I can handle the rest of the problem from there. It's due tomorrow morning, so I greatly appreciate the help.
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  2. #2
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    Quote Originally Posted by Drakeman View Post


    EDIT: And also, this one is kind of stupid, but I'm pretty burnt out and I just can't factor this problem for some reason.

    12x^2 - 36x^3

    Once I get that, I can handle the rest of the problem from there. It's due tomorrow morning, so I greatly appreciate the help.
     12x^2 ( 1 - 3x )

    Does that help?
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