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.

- Feb 23rd 2010, 05:23 PMsammygirl2791Use Lagrange multipliers to find the dimensions of a rectangular box
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.

- Feb 23rd 2010, 05:28 PMicemanfan
So you want to maximize $\displaystyle f(x, y, z) = xyz$ with the constraint that $\displaystyle g(x, y, z) = 4x + 4y + 4z = c$.

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