What are the optimal dimensions for a non-oversized carton with maximum volume?

[physstudent1]

Homework Statement

According to postal regulations, a carton is classified as "over-sized" 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.

Homework Equations

The Attempt at a Solution

I set up the equations.

h + 4x = 108
4x(h)=volume
h=108-4x
432x-16x^2=volume
432-32x=Dv/dx
432=32x
x=13.5
h=54

 

[dynamicsolo]

I set up the equations.

h + 4x = 108
4x(h)=volume

Your equation for the girth seems to agree with the definition you were given.

But your volume equation cannot be correct, because the left hand side will only have units of square inches, while volume is in cubic inches. If the base of this box is a square, what must its volume be?

 

[physstudent1]

oh, should the equation for volume be

x^2(h)=v