A printed page is to contain 60cm² of typing with clear margins around, of 5 by 3. Find the minimum area of the entire page?

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- Nov 26th 2008, 05:29 PMEricCalculus help! Min Max problem
A printed page is to contain 60cm² of typing with clear margins around, of 5 by 3. Find the minimum area of the entire page?

- Nov 26th 2008, 05:59 PMLinnus
$\displaystyle A=xy $

$\displaystyle 60=(x-3)(y-5) $

$\displaystyle \frac {60}{x-3}=y-5 $

$\displaystyle \frac {60}{x-3}+5=y $

$\displaystyle A=x(\frac {60}{x-3}+5)$

Can you do the rest? It's just a matter of taking the derivative of A and doing the first derivative test. - Nov 26th 2008, 06:00 PMmr fantastic
- Nov 26th 2008, 06:05 PMLinnus
Oops, I forgot to take both sides into consideration

$\displaystyle A=xy $

$\displaystyle 60=(x-6)(y-10) $

$\displaystyle \frac {60}{x-6}=y-10 $

$\displaystyle \frac {60}{x-6}+10=y $

$\displaystyle A=x(\frac {60}{x-6}+10)$

Can you do the rest? It's just a matter of taking the derivative of A and doing the first derivative test.

mr fantastic's method works too, except I think he means y+6