Activity 5.3.2.
According to a shipping company’s regulations, the girth plus the length of a parcel they transport for their lowest rate may not exceed \(120\) inches, where by girth we mean the perimeter of one end.
Suppose that we want to ship a parcel that has a square end of width \(x\) and an overall length of \(y\text{,}\) both measured in inches.
(a)
Label the provided picture, using \(x\) for the length of each side of the square end, and \(y\) for the other edge of the package.
(b)
How does the length plus girth of \(120\) inches result in an equation (often called a constraint equation) that relates \(x\) and \(y\text{?}\) Explain, and state the equation.
(c)
Solve the equation you found in (b) for one of the variables present.
(d)
Hence determine the volume, \(V\text{,}\) of the package as a function of a single variable.
(e)
What is the domain of the function \(V\) in the context of the physical setting of this problem? (Hint: neither \(x\) nor \(y\) can equal \(0\text{.}\))
