# Thread: Calculus help! Min Max problem

1. ## Calculus 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?

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

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

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

4. 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