Building a PipelineAn oil company wishes to construct a pipeline from its offshorefacility A to its refinery B. The offshore facility is 2 miles fromshore, and the refinery is 1 mile inland. Furthermore, A and B are5 miles apart, as shown in the figure.A2 mi5 miKX→ImiВThe cost of building the pipeline is $3 million per mile in thewater and $4 million per mile on land. So, the cost of the pipelinedepends on the location of point P, where it meets the shore. Whatwould be the most economical route of the pipeline?Imagine that you are to write a report to the oil companyabout this problem. Let x be the distance shown in the figure.Determine the cost of building the pipeline from A to P and thecost of building it from P to B. Analyze some sample pipelineroutes and their corresponding costs. For instance, what is the costof the most direct route? Then use calculus to determine the routeof the pipeline that minimizes the cost. Explain all steps of yourdevelopment and include any relevant graphs.

Given figure is Length of AP is AP2=22+x2⇒AP=4+x2 Now length of PB is If we increase the side AD to…

Answered: Building a Pipeline An oil company…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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