Applied Optimization: Videos & Practice Problems

A rectangular box with a lid will be constructed from a $20$-inch by $10$-inch piece of cardboard. Two identical squares with side length $x$ inches are removed from each end of the $10$-inch side, and two identical rectangles, each measuring $x$ inches by $y$ inches, are removed from the corners along the $20$-inch side. The remaining flaps are folded upward to form the sides of the box. Let $V\left(x\right)$ represent the volume of the resulting box. Determine the domain of $V$.