Design a rectangular milk carton box of width $w$, length $l$, and height $h$ which holds $470 \text{ cm}^3$ of milk. The sides of the box cost $2 \ \text{cents/cm}^2$ and the top and bottom cost $3\ \text{cents/cm}^2$. Find the dimensions of the box that minimize the total cost of materials used. width = , length = , height = (Include units in your answers.) (Help with units. )