# Thread:

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 $x$, 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
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9006969332695007, "perplexity_flag": "middle"}