Use Lagrange multipliers to find the dimensions of a rectangular box

**sammygirl2791** · February 23rd 2010, 05:23 PM

Use Lagrange multipliers to find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is a constant c.

**icemanfan** · February 23rd 2010, 05:28 PM

So you want to maximize $f(x, y, z) = xyz$ with the constraint that $g(x, y, z) = 4x + 4y + 4z = c$ .

Now use $<\frac{\delta f}{\delta x}, \frac{\delta f}{\delta y}, \frac{\delta f}{\delta z}> = \lambda<\frac{\delta g}{\delta x}, \frac{\delta g}{\delta y}, \frac{\delta g}{\delta z}>$

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