$(15$pts$)$ We want to construct a box with a rectangular base, its length three times the height, and only $60m^2$ of material to use in the construction process. Assuming all the material is used to build the box, determine the maximum volume of the box that can be constructed.

Set up and label$/$identify your constraint and optimization functions.

Define your interval of consideration for the optimization function with respect to the constraint.

Justify how you are coming to your result.

Provide a statement encapsulating the your result.