Minimizing distance problem
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A petroleum refinery is being constructed on the west bank of a conveniently straight river which is 1 km wide. Storage tanks are located on the opposite bank of the river, y = 2 km further south, and need to be connected to the refinery by pipelines. It costs 1 Megadollars/km to lay a pipeline alone the river bank, and 2 Megadollars/km to lay a pipeline under the river. What path should the pipeline follow, in order to minimize the cost?
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Solution Summary
In this solution we are using calculus in order to optimize our outcome. It includes a graph to illustrate the problem.
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Proof.
The pipelines will consist of two parts: A diagonal part under the river that starts from the refinery and goes South-East, and one vertical part that starts ...
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