Results 1 to 2 of 2

Thread: minimums

  1. #1
    Newbie
    Joined
    Jan 2008
    Posts
    12

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    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 $\displaystyle x$, let the height of the page be $\displaystyle y$.

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

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

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

    we have $\displaystyle (x - 2)(y - 5) = 200$ .........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: $\displaystyle x = \frac {200}{y - 5} + 2$

    now, the area of the page is given by:

    $\displaystyle A = xy$

    $\displaystyle \Rightarrow A = \left( \frac {200}{y - 5} + 2 \right)y$ ...........this is what we want to minimize
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. inequalities with maximums and minimums!
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Aug 8th 2010, 06:14 PM
  2. [SOLVED] Local Minimums and Maximums
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 6th 2010, 05:05 PM
  3. Infimum and minimums
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Feb 8th 2009, 06:50 PM
  4. Relative Maximums and Minimums
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Nov 30th 2008, 04:46 PM
  5. [SOLVED] minimums
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jan 6th 2008, 07:26 PM

Search Tags


/mathhelpforum @mathhelpforum