If M=9 and a=3, b=3, c=3 and if we assume the constant P/M^2 to be 1, then P=81 and x=y=z=9 and 81 > 27.

Changing to a=4 and b=2, results in x=16 and y=4. So the increase of a leads to a bigger increase of x (+7) than the decrease of y (-5) caused by the decrease of b.

Hence the price difference is maximized when a=b=c. Because of the squaring, every little increase of one of the weights leads to a bigger increase in price than the decrease in price of the diamond that becomes smaller.

I tried to prove it with the formulas, but I'm stuck at proving that the Max(ab+ac+bc) with M=a+b+c is at a=b=c...