A company needs to run an oil pipline from an oil rig 25 miles out to the sea to

Question

A company needs to run an oil pipline from an oil rig 25 miles out to the sea to a storage tank that is 5 miles inland. The shoreline runs east-west and the tank is 8 miles east of the rig. Assume it costs $50 thousand per mile to construct the pipeline under water and $20 thousand per mile to construct the pipeline on land. The pipeline will be built in a straight line from the rig to a selected point on the shoreline, then a straight light to the storage tank. What point on the shoreline should be selected to minimize the total cost of the pipeline?

Explanation / Answer

let's say the rig is at A
perpendicular to the shore = B
point where pipe line meets the shore = C with BC = x
D is the point 8 mi from B
& E is the storage tank 5 mi inland from B
then AC = sqrt(25^2+x^2)
& CD = sqrt( (8-x)^2 + 5^2)
total cost ('000 $) = 50*sqrt(25^2+x^2) + 20*sqrt((8-x)^2+25)

using the standard calculus approach
value of x for minimum cost ~~5.109 mi <-------

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