The evaluation is based on the thoroughness of the solution, the rigor of method, accuracy of results, use of technology, if needed, to explore the solutions to the problems, communication, and presentation. The report should include a cover page with the names of group members and their student identification numbers, course code, the problem numbers assigned to the group, date of submission, and a citation page at the end including all references used, if any.

$.$The stiffness of a given length of beam is proportional to the product of the width and the cube of the depth. Find the shape of the stiffest beam which can be cut from a cylindrical log $($of the given length$)$with cross$-$sectional diameter of D$.$

Give a problem and solution based on this topic.