The maximum value of the box is 361.186in³
Given,
In the question:
The dimension of the cardboard is given as:
Length of the cardboard is = 23
Width of the cardboard is = 13
and, squares with sides of length x
To find the volume of the largest box that can be formed in this way.
Now, According to the question:
Assume the cut-out is x.
So, the dimension of the box is:
Length = 23
Width = 13
Height = x
The volume of the box will be:
V = (23 - 2x ) (13 - 2x)x
V = 299 - 72x² + 4x³
Differentiate w.r.t to x
V = 299 - 144x + 12x²
Set to 0
V = 299 - 144x + 299 = 0
we have:
x = (2.67, 9.33)
9.33 is greater than the dimensions of the box.
So, the possible value of x is:
x = 2.67
Recall that:
V = 299 - 72x² + 4x³
So, we have:
V = 299 (2.67) - 72 (2.67)² + 4(2.67)³
Hence, the maximum value of the box is 361.186in³
Learn more about Squares at:
brainly.com/question/28776767
#SPJ4
