
differenciation
an offshore oil well is 2 kilometers off the coast. the refinery is 4 kilometers down the coast. laying pipe in ocean is twice as expensive as layiing it on land.
what path should the pipe folow for the minimum cost?
(Lipssealed)
i got 6√3 km from the refinery .. help me whether its right or nt please!

Re: differenciation
No, that's incorrect. Can you show us how you set the problem up?

Re: differenciation
oh, sorry.. i got 7.47..
c= land path + ocean path
d=√(2^2x^2)
L=4x
c(x)= 2√(2^2x^2)+(4x)
differenciation= ((2^2x^2)^1/2)1
when dc/dx=0 , x=1
c(1) =7.47
is it right?

1 Attachment(s)
Re: differenciation
I would draw a diagram first:
Attachment 28122
$\displaystyle O$ represents the under ocean distance and $\displaystyle L$ represents the over land distance. Let $\displaystyle k$ represent the cost per unit length of the over land pipeline.
By Pythagoras we find:
$\displaystyle x^2+2^2=O^2\,\therefore\,O=\sqrt{x^2+4}$
We also know:
$\displaystyle x+L=4\,\therefore\,L=4x$
and so the cost function is:
$\displaystyle C(x)=2kO+kL=k\left(2\sqrt{x^2+4}+(4x) \right)$
This is the function you want to minimize. What do you find when you equate the derivative to zero?