Posted by Calculus on Thursday, October 28, 2010 at 1:17pm.
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 6 km east of the refinery. The cost of laying pipe is $400,000 per km over land to a point P on the north bank and $800,000 per km under the river to the tanks. To minimize the cost of the pipeline, how far from the refinery should P be located? (Round your answer to two decimal places.)

Math Help Please  MathMate, Thursday, October 28, 2010 at 1:36pm
Let the pipe go from R (refinary) to P over a distance of 6x km.
The distance (under water) from P to S (storage) is therefore √(x²+2²).
The total cost, C
C = C1(6x) + C2 (√(x²+2²))
where C1=cost on land
C2 = cost under water, /km
Differentiate C(x) with respect to x and equate to zero for a local minimum.
Solve for x.

Math Help Please  Andrew, Sunday, November 11, 2012 at 3:56pm
x=4.4
Answer This Question
Related Questions
 Math  An oil refinery is located 1 km north of the north bank of a straight ...
 Calc  An oil refinery is located on the north bank of a straight river that is ...
 Calculus  Can anyone help me with these two optimization problems? A boat ...
 physics  A 410mwide river has a uniform flow speed of 2.0 m/s through a ...
 Math  An oil company owns two refineries. The daily production limits and ...
 Pre Calc  From 2 points 400 yards apart on the bank of a straight river flowing...
 MATH  It is a wellknown fact that homing pigeons fly faster over land than ...
 Physics  The captain of a boat wants to travel directly across a river that ...
 Need Help Physics  The captain of a boat wants to travel directly across a ...
 Optimization  A hunter is at a point on a river bank. he wants to get his cabin...
More Related Questions