This is a very interesting calculus word problem that I came across in an old textbook of mine. So I know its got something to do with minimising distance, but other than that, the textbook gave no hints really and I'm really not sure about how to approach it. However, I did manage to make a picture or diagram of it.
Any guidance hints or help would be truly greatly appreciated. Thanks in advance :) So anyway, here the problem goes:
A power house, $P$, is on one bank of a straight river $200\textrm{ m}$ wide, and a factory, $F$, is on the opposite bank $400\textrm{ m}$ downstream from $P$.
The cable has to be taken across the river, under water at a cost of $\text{\$}6/\textrm{m}$.
On land the cost is $\text{\$}3/\textrm{m}$.
What path should be chosen so that the cost is minimized?
Edit: Thanks guys, I think I found out the answer. I shall post it on MSE.