## Calculus 8th Edition

square base of side is $40$ cm and Height is $20$ cm.
Let us consider $V$ be the volume of a box. and $V=xyz$ From the given question: $xyz=32,000$ or, $z=\dfrac{32,000}{xy}$ Consider $f(x,y,z)=xy+2xz+2yz$ and $f_x=y-\dfrac{64,000}{x^2};f_y=x-\dfrac{64,000}{y^2}$ Simplify to get the values of $x$ and $y$ we have $x=64,000y^{-2}, y=64,000x^{-2}$ Solve for $x,y$, we get $x=40,y=40 z=20$ Thus, the square base of side is $40$ cm and Height is $20$ cm.