a) The dimensions of the open box are
Length = 24 - 2x
Width = 12 - 2x
Height = x
b) Recall that the volume of a rectangular prism is given by
[tex]V=l\cdot w\cdot h[/tex]
So, the function for the volume of the open box becomes
[tex]V=(24-2x)\cdot(12-2x)\cdot x[/tex]
c) Let us have a look at the graph of the above function
Notice that the maximum volume of the open box is approximately 332.6 in³
This maximum volume occurs when x is equal to 2.5 in
x = 2.5 in
