Posted by Anom on Wednesday, October 31, 2012 at 2:36pm.
An offshore well is 2 miles off the coast. The refinery is 4 miles down the coast. If a laying pipe in the ocean is twice as expensive as on land, what path the pipe should follow in order to minimize the coast.
Is the answer 2.1? Can you some list their steps?
- Calculus - Reiny, Wednesday, October 31, 2012 at 4:19pm
Make a sketch, mark the well as W and the point on the shore closest to W as A, label the refinery as R
Place P somewhere between A and R.
They will lay the pipeline from R to P along the shore, then directly through the water to W
let AP=x , the PR = 4-x, and AW=4
WP = √(9-x^2) or (9-x^2(^(1/2)
cost = 1(4-x) + 2(9-x^2)^(1/2) , the actual money units don't matter as long as they are in the ratio 1 : 2
d(cost)/dx = -1 + (1/2)(9 - x^2)^(-1/2) (-2x)
= 0 for a min of cost
1 = x/√(9-x^2)
x = √(9-x^2)
square both sides
x^2 = 9-x^2
2x^2 = 9
x^2 = 4.5
x = √4.5 = appr 2.12
So they should aim for a point P which is 2.12 miles from A or 1.88 miles from R
Answer this Question
More Related Questions
- Calculus - Optimization An offshore oil well is 2km off the coast. The refinery ...
- math - You are asked to design a piping system that will connect a drilling rig ...
- Calculus - A man is in a boat 4 miles off a straight coast. He wants to reach a ...
- Calculus - You are in a boat "a" miles from the nearest point on the coast. You ...
- math - a man is in a boat 2 miles from the nearest point on the coast. He is to...
- Math(module 4 Calculus) - (minimum commuting time) A lighthouse lies 2 miles ...
- calculus - Given ensuing information, determine the least cost and the least ...
- Math - A distressed ship is 10 miles south and 8 miles east of a coast guard ...
- Science - which of these statements provides evidence to the fact that oceans ...
- Math - In the Atlantic ocean off the coast of Bermuda lies a 500,000 square mile...