1. The problem statement, all variables and given/known data A rectangular beam is cut out of a cylindrical log with diameter 30cm. Given that the strength of a beam is jointly proportional to its width and the square of its depth, find the dimensions of the beam with maximum strength. 2. Relevant equations implicit differentation 3. The attempt at a solution Frankly, I do not know where to start with this question. I think it's the strength reference that threw me off from this. From what I can tell, S is equal to w+d^2 (where S is strength, w is width and d is depth). Next I need to find another relation to end up with one variable to successfully use the Algorithm for Extreme Values and then find the dimensions. I know I will have to bring the diameter of the log into the problem here somehow, but I am not sure how to do this. If anyone could be of help here it would be great. Thanks in advance.