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Minimization problem applied to two factories

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Two factories are located at the coordinates (-x,0) and (x,0), with their power supply located at (o,h). Find y such that the total amount of power line from power supply to the factories is a minimum.

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Solution Summary

This important problem is solved giving all necessary mathematical steps. It will enable you to do similar problems yourself.

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Please view the figure first and read on..

Let L = total length of the power line

from the figure, the total length of the red line = sqrt(x^2 + y^2) + sqrt(x^2 + y^2)

(we used the formula, hypotenuse = sqrt(base^2 + ...

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