Calculus - Oil Rig Optimisation

[#anon]

​

The oil-well is 6km off shore. The refinery is on the coast, 8 km from the nearest point of land to the oil well. The costs is $ S per km to lay pipe along the shore but U times as much per km to lay pipe underwater. Pipe may be laid either straight to the refinery, or to an intermediate point on the coast then along the coast.

The question asks me to find the total cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore.

I came up with S(8 - x) + U sqrt(x ^ 2 + 36) but its not right and I can't find out what I did wrong.

Any help would be much appreciated.

 

[Deleted member 4993]

​

The oil-well is 6km off shore. The refinery is on the coast, 8 km from the nearest point of land to the oil well. The costs is $ S per km to lay pipe along the shore but U times as much per km to lay pipe underwater. Pipe may be laid either straight to the refinery, or to an intermediate point on the coast then along the coast.

The question asks me to find the total cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore.

I came up with S(8 - x) + U sqrt(x ^ 2 + 36) but its not right and I can't find out what I did wrong.

Any help would be much appreciated.

Can you please tell us - how did you get total cost = S(8 - x) + U sqrt(x ^ 2 + 36)

How do you know that it is not the correct answer?

What was your interpretation of that statement?

 

[#anon]

Its an online question.
I have calculated the formula.

(S*U*sqrt(x ^ 2 + 36)) + S*(8 - x)

 

[stapel]

Its an online question.

Okay. But that doesn't answer any of the questions you were asked in this thread. Please reply with that information.

I have calculated the formula.

(S*U*sqrt(x ^ 2 + 36)) + S*(8 - x)

Okay. But that doesn't answer how you "calculated" this formula. Please reply with that information.

Thank you!