Question 990438
The volume of the rectangular box is (120-2x)(80-2x)*x cm^3
This is (9600-400x+4x^2)*x
V=4x^3-400x^2+9600x
Take the first derivative and set it equal to zero
12x^2-800x+9600=0
4(3x^2-200x+3200)=0
The vertex (minimizes x) is at x=200/6=33.3 cm must be cut  (33 1/3 is exact)
The volume is 13.3*53.3*33.3 (units cm for each)
{{{graph(300,300,-10,50,-50,70000,4x^3-400x^2+9600x)}}}