What is the Optimal Solution for a Wire Length Minimization Problem?

[opticaltempest]

I am having trouble setting up the primary equation to this optimization problem.

Here is a link to the problem
http://img293.imageshack.us/img293/806/appliedminmaxprob5vo.jpg"

Here is the best equation I can come up with but this leads me nowhere...

The hypotenuse of the each triangle: sqrt(x^2+y^2)
The length of the line from (0,h) to (0,y): h-y

let L be the length of the wire needed then

L = 2sqrt(x^2+y^2)+h-y

2sqrt(x^2+y^2) for the two hypotenuses of the triangles
h-y for the small line segment from point (0,h) to (0,y)

Where can I go from here? I'm only looking for a small hint to get me going in the right direction... Thanks

 

[hotvette]

Looks good so far. The clue for the next step is in the question, which is to find y such that the length of power line is minimized. Hint: a derivative is involved.

 

[HallsofIvy]

Remember that x and h are given constants. It is only y that is a variable. Your answer will depend on x and h.

 

[opticaltempest]

Here is my final solution so far...
It's 5 pages but I tried to explain what I was doing in detail :)
Please comment on my mathematical writing as well as my solution.
I really want to improve my mathematical writing.
Thanks

http://img434.imageshack.us/img434/6807/solutionpart16fp.jpg"

http://img434.imageshack.us/img434/9853/solutionpart26xc.jpg"

http://img434.imageshack.us/img434/4665/solutionpart39cr.jpg"

http://img434.imageshack.us/img434/2691/solutionpart41om.jpg"

http://img434.imageshack.us/img434/1182/solutionpart56qq.jpg"



/math rocks
//off to watch The Daily Show
////why am i doing this
/////I read to much fark.com