# Math Help - Max Min Calc Problem

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

3. ## 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

4. ## Re: Max Min Calc Problem

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

5. ## Re: Max Min Calc Problem

thanks for the picture

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