Final answer:
To find the least expensive rectangular box, use the formula lwh and make the length, width, and height as close to each other as possible.
Step-by-step explanation:
The dimensions of the least expensive rectangular box can be found using the formula lwh. In this formula, l represents the length, w represents the width, and h represents the height of the box.
To find the least expensive rectangular box, we need to minimize the cost of materials used. This means we need to minimize the surface area of the box, which is given by the formula 2lw + 2lh + 2wh. To minimize the surface area, we can use calculus or simply make the length, width, and height as close to each other as possible.
Therefore, the dimensions of the least expensive rectangular box are l = w = h.