Volume Find the dimensions of a rectangular package of maximum volume that may be sent by a shipping company, assuming that the sum of the length and the girth (perimeter of a cross section) cannot exceed 96 inches.
To calculate: The dimensions of a rectangular package such that the volume is maximum and whose sum of the length and the girth cannot exceed
Given Information:
A rectangular package has a sum of length and girth that does not exceed
Formula used:
Consider a package (rectangular) of the following dimensions,
Then the volume is
Also, if there is a function
Step1:
Step2:
Calculation:
Let the length of the rectangular package be x, width be y and height be z.
A rectangular package has a sum of length and girth that does not exceed
Now, the volume of the package is
So,
Now find partial derivative of V with respect to y and z,
And,
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