I have a few questions - Engineering

[Ego]

Here's the picture of the assignment:
http://img172.imageshack.us/my.php?image=hw8nm2.jpg

I need to design the water treatment plant to be between both of the cities equally. I'm a bit confused on where to place the plant on the line(Lake shore). I know that you could derive the formula to find the tangent point but that wouldn't tell me where to place the treatment plant or would it?

Also once I figure out where to place the plant and basically make two right triangles do I use trig to figure out the distance from the road to the plant and how long the pipes need to be to reach each city?

If anyone could help me with the formula to figure out where to place the plant and what do after I make two right traingles to get the distance, I probably will be good to go.

TIA,
Aaron

 

[Pyrrhus]

what are the guidelines the problem states you should consider??

 

[huckmank]

Well, you want to find the minimum for the (cost of the road) + (cost of the pipeline). The road will simply form a 90% angle with the current highway (x-axis), while the pipeline will be two hypotenuses of two right angle triangles with bases of E/W Highway. So you need to set up an optimization problem with the (cost of pipeline)(pipeline length) + (cost of road)(road length) and find the minimum cost.

As for the formula for the pipeline length. What does Pythagorus have to say about the length of a hypotenuse?

You should be able to take it from there.

 

[Ego]

Thanks for the responses guys but fortunately I asked one of my class mates that happens to take some of the same classes as me and he set me straight. I got it all completed last night.

Thanks again,
Aaron