# Max Min Calc Problem

• September 26th 2011, 12:42 AM
jaykobhxc
Max Min Calc Problem
Hey all,

I am in a sticky situation at the moment involving a min/max calculus problem.
the problem goes as follows.

An offshore oil well must be connected by pipe to the refinery. The oil-well is 3 km off-shore. The refinery is on the coast, 6 km from the nearest point of land to the oil well. It costs $S per kilometer to lay pipe along the shore, but U times as much per km to lay pipe underwater. The pipe may be laid either straight to the refinery or to an intermediate point on the coast then along the coast. Give the total cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This should be a formula involving x, S and U. Now I have considered a right angled triangle with U length on one side and S on the other and x being the hypotenuse. Now with that being the case, x^2 = u^2 + s^2 so x = sqrt(u^2 + s^2) with 0 < u < 3 and 0 < s < 6. However the question says cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This is the bit I’m struggling to comprehend. Any help would be greatly appreciated! • September 26th 2011, 01:41 AM CaptainBlack Re: Max Min Calc Problem Quote: Originally Posted by jaykobhxc Hey all, I am in a sticky situation at the moment involving a min/max calculus problem. the problem goes as follows. An offshore oil well must be connected by pipe to the refinery. The oil-well is 3 km off-shore. The refinery is on the coast, 6 km from the nearest point of land to the oil well. It costs$ S per kilometer to lay pipe along the shore, but U times as much per km to lay pipe underwater. The pipe may be laid either straight to the refinery or to an intermediate point on the coast then along the coast.

Give 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. This should be a formula involving x, S and U.

Now I have considered a right angled triangle with U length on one side and S on the other and x being the hypotenuse. Now with that being the case, x^2 = u^2 + s^2 so x = sqrt(u^2 + s^2) with 0 < u < 3 and 0 < s < 6.

However the question says cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This is the bit I’m struggling to comprehend. Any help would be greatly appreciated!

Have you drawn a picture? U and S are costs per km of pipe how do you get to use them as lengths?

The length of pipe under water is $\sqrt{x^2+3^2}$ km then length of pipe on shore is $(6-x)$ km.

CB
• September 26th 2011, 02:13 AM
jaykobhxc
Re: Max Min Calc Problem
Yes i have drawn a picture and just got totally bamboozalled!

Give 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. This should be a formula involving x, S and U. i'm still confussed on what to do there :(
• September 26th 2011, 03:07 AM
CaptainBlack
Re: Max Min Calc Problem
Quote:

Originally Posted by jaykobhxc
Yes i have drawn a picture and just got totally bamboozalled!

Give 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. This should be a formula involving x, S and U. i'm still confussed on what to do there :(

How long is the pipe run under water?

How long is the pipe run along the shore?

How much do each of the runs cost?

What is the total cost?

CB
• September 27th 2011, 04:28 AM
jaykobhxc
Re: Max Min Calc Problem
thanks for the picture :)

so would the formula be u*sqrt(3^2 +x^2) + s*(x-6)?