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 6-x km.
The distance (under water) from P to S (storage) is therefore √(x²+2²).
The total cost, C
C = C1(6-x) + 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