Calc 1 help?

Question

This is a opptimization problem
The US. postal service will accept a box for domestic shipment only if the sum of its length and girth does not exceed 108. What dimensions will give a box with a square end the largest possible volume.
Please describe how you arrived at the answer

Answer 1

Let x = side of square base
Let = length
Then girth = 2(l+x) = 2l+2x = 108, so
l+x = 54
V = x^2l= x^2(54-x)
V = 54x^2-x^3
dV/dx = 108 x - 3x^2
Set dV/dx = 0 getting:
3x^2 = 108 x
3x = 108
x= 36 = side of square base
l= 54-36 = 18 = length