# Optimization: Beam of maximum strength

1. Nov 14, 2005

### HappMatt

first off here is the problem
:18. A rectangular beam is cut from a cylindrical log of radius 30 cm. The strength of a beam of width w and height h is proportional to . Find the width and height of the beam of maximum strength.
so I have a diagram of it but im having troubles setting up the problem. But i just cant figure out how to set it up. I think that one of the equations i need would be (h*w)/(wh^2) not sure if thats right and then for the sides i figure you have to use the pythagorean identity to get h=(30^2-w^2)^(1/2) from here im lost and have obviously given up hope of solving it on my own. P.S. i absoulutly hate this stupid huges-huallete/wiley single variable calc book, the book suck, or mybee i do.

- wel im still staring at the problem and this time i came up with something new. I though mybe i was reading the proportional part wrong and that mybee (w*h^2) is the proportion and that all i need it the deriv of that maximized at 0 then plug in h=(30^2-w^2)^(1/2) to figure out where the height is maximized. i also added some work so you all dont just think im a lazy bastard.

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Last edited: Nov 14, 2005
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