According to postal regulations, a carton is classified as "oversized" if the sum of its height and girth (the perimeter of its base) exceeds 108 in. Find the dimensions of a carton with square base that is not oversized and has maximum volume.

18" X 18" X 36"

Step-by-step explanation:

Given a square base container of height h, let a side of the base =s

The volume of the container,

If the sum of its height and girth (the perimeter of its base) equals 108 in

Substituting h=108-4s into V

We are required to determine the maximum volume of such container, first we take the derivative:

Optimizing:

Recall that: h = 108-4s

The dimensions of the carton are 18" X 18" X 36".

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step-by-step explanation: