# 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

#### Solution Preview

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.

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#### Solution Summary

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

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