Question 1122183
V=l*w*h
draw this out, and cut a square with side x out of each of the 4 corners.
the length of the box will be 8-2x and the width 3-2x.  The height is x
The volume is (24-22x+4x^2)*(3-2x)=(24-22x+4x^2)x
=4x^3-22x^2+24x
take the derivative and set equal to 0
0=12x^2-44x+24
divide by 4
3x^2-11x+6=0
(3x-2)(x-3)=0
x=(2/3), and 3, but 3 inches is the entire width, so x=1/3 inch
volume is (6 2/3)(1 2/3) (2/3)=200/27 in^3=7.41 in^3

{{{graph(300,300,-2,2,-10,10,4x^3-22x^2+24x)}}}