1. ## Optimization Problem

This problem has been giving me a lot of trouble, mostly because I am unsure how to set it up in order to find the minimum value.

Two posts, one$\displaystyle 12ft$ high and one $\displaystyle 28ft$ high, stand $\displaystyle 30ft$ apart. They are to be stayed by two wires attached to a single stake, running from ground level to the top of each post. Where should the stake be placed to use the least amount of wire?

I'm not really sure how to set this up besides this diagram:

2. Originally Posted by ~berserk
This problem has been giving me a lot of trouble, mostly because I am unsure how to set it up in order to find the minimum value.

Two posts, one$\displaystyle 12ft$ high and one $\displaystyle 28ft$ high, stand $\displaystyle 30ft$ apart. They are to be stayed by two wires attached to a single stake, running from ground level to the top of each post. Where should the stake be placed to use the least amount of wire?

I'm not really sure how to set this up besides this diagram:
This should get you started

let $\displaystyle x$ be the distace the peg is from the 12ft pole. Then the distance from the peg to the 28ft pole is $\displaystyle 30-x$

Now use the pythogrean theorem to find the lenth of each hypotenuse.

Good luck!