According to U.S. postal regulations, the girth plus the length of a
parcel sent by mail may not exceed 108 inches, where by "girth" we
mean the perimeter of
the smallest end.
What is the largest possible volume of a rectangular parcel with a square
end that can be sent by mail? Such a package is shown below, with x and y measured in inches. Assume y>x .
What are the dimensions of the package of largest volume?

Find a formula for the volume of the parcel in terms of

Volume =

The problem statement tells us that the parcel's girth plus length may not exceed
108 inches. In order to maximize volume, we assume that we will actually need the
girth plus length to equal 108 inches. What equation does this produce involving

Equation:

Solve this equation for

Find a formula for the volume

What is the domain of the function

Domain:

Find the absolute maximum of the volume of the parcel on the domain you
established above and hence also determine the dimensions of the box of greatest
volume.

Maximum Volume =

Optimal dimensions:

You can earn partial credit on this problem.