Originally Posted by

**Zion** Hello, I am stuck on a problem and need a bit of help.

An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east of the refinery. The cost of laying pipe is $400,000/km over land to a point P on the north bank and $800,000/km under the river to the tanks. To minimize the cost of the pipeline, where should the point P be located?

Here is what I have so far.. (sorry for the drawing, I'm new to this and don't know of any better way to do it) EDIT: Drawing didn't transfer very well from the edit box

I know that

$\displaystyle Cost = 400,000x + 800,000y$

and

$\displaystyle y = sqrt(2^2 +(6-x)^2)$

and I know that to find the min we need to find $\displaystyle dC/dx$ and set equal to 0 but when I do this I get stuck when solving for x. Maybe I'm messing up my algebra, I don't know, but any help would be appreciated.

Thanks