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    Lagrange multipliers

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    A hot water tank is a vertical cylinder surmounted by a hemispherical top of the same diameter . The tank is designed to hold 750m^3 of liquid.

    Determine using Lagrange multipliers the total height and the diameter of the tank if surface heat loss is to be a minimum.

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    https://brainmass.com/math/geometry-and-topology/lagrange-multipliers-hemispherical-top-291824

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    Let r be the tank's radius and h the cylinder's height.
    The volume ...

    Solution Summary

    Lagrange multipliers are employed.

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