Question 201030
A  rough  sketch  of  the  net  will  help.
It  is  a  square,  30 x 30,  with  square  cutouts  at  each  corner.
The  cutouts  are  x by x.
This  makes  the  base  (30-2x)  square
.
The  volume  of  the  folded  box  is  ,,,Vol  =  L*W*h = (30-2x)(30-2x)(x)
.
V = {900 -120x +4x^2} *x
.
V= 4x^3 -120x^2 +900x
.
a  table  of  options  
.
x,,,,,,,,,,Volume
0,,,,,,,,,0
1,,,,,,,784
2,,,,,,1352
3,,,,,,1728
4,,,,,,1936
4.9,,,,1999
5,,,,,,2000,,,,,,max
5.1,,,,1999
6,,,,,,1994
10,,,,,1000
15,,,,,,,,0
.
Therefore  max  box  is  20 x 20 x 5 =2000  cubic  inches