Optimization Problem: A = l*w - Tips & Advice

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The problem:
6a5e211c2333b0c4fdf530d54f61c015.png

Relevant Equations:
A = l * w

So I drew a rectangle like this:
36e9aa450e032dab13d9c3d0eaf4252e.png

And I'm not really sure how to proceed from this point.. I always have a hard time setting up the problems for optimization :/

Any tips to the right direction would be greatly appreciated! Just to clarify, this is non-integration optimization. (And any advice about optimization in general would be welcomed too!)
Thankyou!
 
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Homework or textbook problems should be posted in the Homework & Coursework sections, not in the technical math sections. I have moved your thread to the appropriate forum section.
 
Mark44 said:
Homework or textbook problems should be posted in the Homework & Coursework sections, not in the technical math sections. I have moved your thread to the appropriate forum section.
Oops, I haven't been on for a while and am readjusting to the forums new style, my bad! I'll make sure to post in the correct sections next time! Thanks.
 
Kitty Kat said:
The problem:
6a5e211c2333b0c4fdf530d54f61c015.png

Relevant Equations:
A = l * w

So I drew a rectangle like this:
36e9aa450e032dab13d9c3d0eaf4252e.png

And I'm not really sure how to proceed from this point.. I always have a hard time setting up the problems for optimization :/

Any tips to the right direction would be greatly appreciated! Just to clarify, this is non-integration optimization. (And any advice about optimization in general would be welcomed too!)
Thankyou!
From your drawing, what are the dimensions of the piece of paper?
What equation can you write that gives the area of the piece of paper in terms of the paper dimensions?
What equation can you write that gives the area of the part of the paper where text will appear?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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