1. ## 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

2. Originally Posted by chibiusagi
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