Homework Help: Calc

Posted by Aaron on Monday, November 30, 2009 at 10:28pm.

An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 3 km east of the refinery. The cost of laying pipe is $300,000 per km over land to a point P on the north bank and $600,000 per km under the river to the tanks. To minimize the cost of the pipeline, how far from the refinery should P be located? (Give your answer correct to two decimal places.)

Calc - MathMate, Tuesday, December 1, 2009 at 12:35am
Let x be the distance between P and a point on the north bank directly opposite to the tanks.

The length of the pipe under water,
L1(x) = √(2²+x²).
The length of the pipe on land,
L2(x) = 3-x
Cost of laying the pipes,
C(x) = 600000 L1(x) + 300000 L2(x)

Differentiate C(x) with respect to x and equate the derivative to zero.
Solve for x.
The distance from the refinery to P is (3-x).
I get about 1.8 km.

Answer this Question

Related Questions

Math - An oil refinery is located 1 km north of the north bank of a straight ...
Math Help Please - An oil refinery is located on the north bank of a straight ...
Calculus - Can anyone help me with these two optimization problems? A boat ...
physics - A 410-m-wide river has a uniform flow speed of 2.0 m/s through a ...
Pre Calc - From 2 points 400 yards apart on the bank of a straight river flowing...
vectors components - plz answer my question a river is 2 km wide and flows at ...
Math - How do I draw the following problem so I have something to refer to when ...
calculus - A man launches his boat from point A on a bank of a straight river, 3...
Vectors - a river is 2 km wide and flows at 4km/h. a motorboat has a speed of 10...
MATH - It is a well-known fact that homing pigeons fly faster over land than ...

For Further Reading

First Name:
School Subject:
Answer: