## Calculus 8th Edition

$\dfrac{c}{12}$
Need to apply Lagrange Multipliers Method to determine the dimensions of a rectangular box of maximum volume. we have $\nabla f=\lambda \nabla g$ The volume of a box is $f=V=xyz$ and From the given question let us consider $g=4x+4y+4z=c$ Now, $\lt yz,xz,xy \gt =\lambda \lt 4,4,4 \gt$ Simplify to get the values of x,y and z. $y=x,z=x$ $4x+4y+4z=c$ $4x+4y+4z=c$ $x=\dfrac{c}{12}$ Thus, Box is a cube with edge length: $c=$ $\dfrac{c}{12}$