Mathgirl, question!

[KillerMuffin]

Okay, stupid, stupid question. Well, it's not a stupid question, it's just stupid of me to be asking this question now considering that I'm going to get up, go get in the car, and toodle my happy little ass right on down to school and turn this in right after I hit the "post thread" button here. So it's not like I can actually do anything with the answer to the question except say "ooooohhh!" in that dumbfounded, oh-my-gawd-that-was-so-simple, how-could-I-have-missed-that! voice.

Add on to that the fact that this is my last semester, actually, my last month as a computer science major (long story; incredibly boring to boot) so it's not like I'm actually going to need this stuff. Well, maybe on the final. At any rate. Here's my question!

54. Minimum Cost

An offshore oil well is 2 kilometers off the coast. The refinery is 4 kilometers down the coast. If laying pipe in the ocean is twice as expensive as on land, what path should the pipe follow in order to minimize the cost?


Note: We have just finished the whole first derivative, second derivative, let's draw graphs of problems with way too many square roots for comfort thing. We are applying this to "real world" situations in the form of what they c

Gotta go, the StudMuffin is honking. He thinks he can a 50 mile round trip done in time to get back for Dragonball Z. Shya right.

 

[NoJo]

The pipe should enter the sea sqrt(4/3) = 1.154 km towards the refinery.

If the cost is $1,000 per km on land and $2,000 in the sea, this gives the minimum total cost of $7,464.

Making the pipe straight (so all of it goes in the sea) would cost $8,944, ($2,000*sqrt(20))

Making it go into the sea at right angles (i.e. as short a lenght as possible in the sea) would cost $8,000.

 

[KillerMuffin]

And ya beat her to it.

Thanks SJ!

That actually helps immensely.

 

[MathGirl]

And ya beat her to it.

<Blush>

 

[The_old_man]

This answer of course does nottake into consideration the $15000.00 for the Environmental Impact Study required, the $25000 for legal fees to fight the local NIMBY resistance suits, etc.

 

[Pure]

X is the distance towards the refinery.

Cost is a multiple of (4-x) + 2(4+x**2)**(1/2) = y

Distance on land plus the hypotenuse of the triangle doubled.

y' =-1 + (2x)(4+x**2)**(-1/2)

Setting = 0, multiplying by radical

-(4+x**2) +2x =0

4+x**2 = 4x**2

x**2 =4/3 or x=2/3**.5

1.154 as sub joe stated.

 

[Un-registered]

This answer of course does nottake into consideration ... the $25000 for legal fees to fight the local NIMBY resistance suits, etc.

I think you missed a zero out there. $250,000 is nearer the mark.

 

[MathGirl]

FLOHIW

Dear KMuffin,
I hope you passed your calc course with flying colors. Fat lot of help I was.
MG

 

[The_old_man]

Did not drop a decimal. I was using the same dollars as quoted for construction costs.