Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. Suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 168 cm. A passenger wants to take a box of the maximum allowable volume. If the length and width are to be equal, what should the dimensions be?
length = width =
height =
In this case, what is the volume?
volume =
(for each, include units)

If the length is be twice the width, what should the dimensions be?
length =
width =
height =
In this case, what is the volume?
volume =
(for each, include units)