A pipeline is to be placed so that it connects point A to the river point B. A and B are two homesteads and X is the pumphouse. How far from M should X be so that the pipeline is as short as possible?

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- Nov 25th 2009, 12:21 PMshawlioptimization - distance on a pipeline
A pipeline is to be placed so that it connects point A to the river point B. A and B are two homesteads and X is the pumphouse. How far from M should X be so that the pipeline is as short as possible?

- Nov 25th 2009, 01:40 PMgalactus
Use a little Pythagoras on the two right triangles.

Let L=length of pipeline. Let x=length from M to X.

$\displaystyle L=\sqrt{1+(5-x)^{2}}+\sqrt{x^{2}+4}$

Differentiate, set to 0 and solve for x