Answer:
The volume in such a package is 10,415.41 in³
Explanation:
Consider the provided information.
A parcel delivery service will deliver a package only if the length plus the girth (distance around, taken perpendicular to the length) does not exceed 104 inches.
Let the dimension are x by x by y.
Where x is the variable for the square base package and y is the variable for length.
Thus l=x, b=x and h=y
Then the volume of the box is:
(∵V=lbh)
The maximum combined length and girth is 104.
Therefore,


Substitute the value of y in volume of the box.



Substitute V'(x)=0.



Now apply second derivative test.

(Min)
(Max)
If x=52/3 then

Substitute x = 52/3 and y = 104/3 in


Hence, the volume in such a package is 10,415.41 in³