### Home > PC3 > Chapter Ch8 > Lesson 8.1.2 > Problem8-29

8-29.

The volume of an open-top box is $30\text{ in}^3$. The length of the base is twice the width.

1. Sketch a labeled diagram.

Sketch a box. Label the height $h$ and the sides of the base $x$ and $2x$.

2. Express the total outside surface area, $S$, in terms of the width, $x$. Simplify.

$S=x·2x+x·h+2x·h+x·h+2x·h$

3. What width will minimize the surface area?

Graph your function from part (b) and locate the minimum point.