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Differential Calculus: Maximum and Minimum Problem and Solution

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 $200,000 per km over land to a point P on the north bank and $400,000 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. ) 1 year ago Report Abuse Colorado… Best Answer – Chosen by VotersThis is a min-max calculus problem, where we want to minimize the cost function: We need a drawing of the situation: see https://docs. google. com/drawings/d/1PvkU… where R is the refinery, O will be the x-axis origin, P is the point on the north bank, and x= distance from O to the storage tanks.

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