Consider the girth first, it is the shortest distance around the parcel. And then L is the longest side. Based on the dimensions, this gives us two sets of possible equations. The first, if x is the longest side, gives us this:
Or, if y is the longest:
Alright, I left off here! Let me know if you need a hand with the other question, it is just differentiation and finding a maxima, give it a go!
So here, we have two potential equations to start with, let's see how they effect the formulae for volume (in both cases, we'll eliminate y):
When we do this, it becomes a little clearer that the top option gives a larger volume for any value of x. I'll leave you to form a mathematical proof with all this information, but that's the basic setup!
To show you the idea of finding the maxima/minima, I'll work through this one for you:
So the dimensions are (using the formulas above), 50/3 by 50/3 by 100/3