Finding Applied Minimum of a Poster (Calculus Word Problem)

• November 2nd 2008, 06:20 PM
Drakeman
Finding Applied Minimum of a Poster (Calculus Word Problem)
I've been doing pretty good on these Min/Max problems so far, but this one is kind of getting to me. It goes like this:

Quote:

Determine the minimum area of a poster that will contain 50 square inches of printed material and have 4 inch margins on the top and bottom and 2 inch margins on the left and right. Prove your answer.
I was able to draw out a rectangles and define the x and y sides while filling in the appropriate labels. It looks like this:

It's very messy, and I apologize for that, but it's the best I could do and it fits the description I gave. How do I go about setting this one up so I can find the derivative, factor it, get the points (min and max), and find the restrictions?

EDIT: And also, this one is kind of stupid, but I'm pretty burnt out and I just can't factor this problem for some reason.

$12x^2 - 36x^3$

Once I get that, I can handle the rest of the problem from there. It's due tomorrow morning, so I greatly appreciate the help.
• November 2nd 2008, 06:28 PM
kpizle
Quote:

Originally Posted by Drakeman

EDIT: And also, this one is kind of stupid, but I'm pretty burnt out and I just can't factor this problem for some reason.

$12x^2 - 36x^3$

Once I get that, I can handle the rest of the problem from there. It's due tomorrow morning, so I greatly appreciate the help.

$12x^2 ( 1 - 3x )$

Does that help?