What would be the MAX. volume of a box that weighs 100 lb max, but is less than (lenght x width x depth) / 166

Question

I know they taught me this in Calculus 1 but i flunked for a reason! I actually need this to ship some things (clothes, shoes, stuffed animals,etc.) from the US to my hometown

Answer 1

The maximum weight is simply a constraint you have to adhere to when filling the box. It doesn't enter into the calculation. It is general knowledge(and can be shown with calculus) that when the linear dimensions are treated equally(such as length x width x depth) that the volume is maximum when the dimensions are equal. So the answer is:
Maximum volume is achieved when the box has the shape of a cube.

If you're saying that the volume has to be less than 166 cubic inches, then:
l x w x h < 166
Assuming the shape of a cube:
s^3 < 166
s < 5.49 inches

Your statement looks like it's saying:
V < l x w x h/166
But that doesn't make sense because:
V = l x w x h