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Math Help - minimums

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    Exclamation minimums

    HELP !!! ><><

    A printed page of a book is to have side margins of 1cm, a top margin of 2 cm and a bottom margin of 3 cm. IT is to contain 200cm^2 of printed matter, Find the dimensions of the page if the area of the paper used is to be a minimum
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by chibiusagi View Post
    HELP !!! ><><

    A printed page of a book is to have side margins of 1cm, a top margin of 2 cm and a bottom margin of 3 cm. IT is to contain 200cm^2 of printed matter, Find the dimensions of the page if the area of the paper used is to be a minimum
    let the width of the page be x, let the height of the page be y.

    then, the width of the printed area is (x - 2) ....why is that?

    and the length of the printed area is (y - 5) .....why is that?

    since the area of the printed material is 200 \mbox{cm}^3

    we have (x - 2)(y - 5) = 200 .........this is our constraint equation. we can use this to solve for one variable in terms of the other. for instance, solving for x we get: x = \frac {200}{y - 5} + 2

    now, the area of the page is given by:

    A = xy

    \Rightarrow A = \left( \frac {200}{y - 5} + 2 \right)y ...........this is what we want to minimize
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