If anyone can solve this...

[Thepiman]

A pipeline needs to be laid between an offshore oil rig (A) to the refinery (B) on the coast (length NB). It costs 5 times as much to lay a mile of underwater pipeline as it does to lay a mile of pipeline on land.


REFER TO ATTACHED IMAGE


The distance AN is 50 km and distance NB is 100 km. The plan is to lay the pipeline as a straight stretch AM underwater followed by a straight stretch MB on land as above. Determine where point M should be if the pipeline is to be laid as cheaply as possible?

 

[lookagain]

A pipeline needs to be laid between an offshore oil rig (A) to the refinery (B) on the coast (length NB).
It costs 5 times as much to lay a mile of underwater pipeline as it does to lay a mile of pipeline on land.


REFER TO ATTACHED IMAGE


The distance AN is 50 km and distance NB is 100 km. The plan is to lay the pipeline as a straight stretch AM underwater followed
by a straight stretch MB on land as above. Determine where point M should be if the pipeline is to be laid as cheaply as possible?

Thepiman, you need some one-on-one help. And you haven't shown any work here.
The ability to differentiate an expression for this problem is already expected.

From these other threads of yours on here, you don't even know what differentiation is:


http://www.freemathhelp.com/forum/threads/87098-Differentiation

http://www.freemathhelp.com/forum/t...ion-with-electricity-help?p=357272#post357272

 

[mmm4444bot]

Hello Thepiman:

Where are you stuck?

Please take a moment to read the forum guidelines; you can start at this link to the summary page.

Thank you! :cool:

PS: The first step in this exercise is to write a function that inputs the distance from N to M (you could call it x) and outputs the cost of the entire pipeline.

 

[Quaid]

It costs 5 times as much to lay a mile of underwater pipeline as it does to lay a mile of pipeline on land.

Is it the fact that no dollar amounts are provided that's confusing?

The position of M which minimizes overall cost will be the same, regardless of the actual dollar amounts involved. You're not asked to quote the cost; just the position of M (i.e., the distance from N to M).

Therefore, you could multiply the length of the underwater pipe by 5, and then add that result to the pipe length on land, to get your cost function.

Then differentiate and find the critical point, in the usual way.

Cheers