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    Optimization for trapezoid

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    A trough with trapezoidal cross sections is formed by turning up the edges of a 30 inch wide sheet of aluminum. Find the cross section of maximum area.
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    https://brainmass.com/math/optimization/optimization-trapezoid-23048

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    See attachment please!

    Solution. Denote the area of the cross section by S. Then we have

    Obviously, is a function with two variables such that .
    Now we are going to find its maximum. First, we need to find the partial derivatives.

    ...

    Solution Summary

    This shows how to find the cross section of maximum area for a given solid.

    $2.49

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