Calculus help! Min Max problem

**Eric** · November 26th 2008, 05:29 PM

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?

**Linnus** · November 26th 2008, 05:59 PM

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

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

**mr fantastic** · November 26th 2008, 06:00 PM

Originally Posted by Eric

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?

Minimise $A = (x + 10)(y + 6)$ subject to the condition $xy = 60$ .

**Linnus** · November 26th 2008, 06:05 PM

Oops, I forgot to take both sides into consideration

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

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

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