- #1
Emethyst
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Homework Statement
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.
Homework Equations
implicit differentation
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.