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Answer:
The dimensions of the box that minimize the materials used is
Step-by-step explanation:
Given : An open top box is to be built with a rectangular base whose length is twice its width and with a volume of 36 ft³.
To find : The dimensions of the box that minimize the materials used ?
Solution :
An open top box is to be built with a rectangular base whose length is twice its width.
Here, width = w
Length = 2w
Height = h
The volume of the box V=36 ft³
i.e.
The equation form when top is open,
Substitute the value of h,
Derivate w.r.t 'w',
For critical point put it to zero,
Derivate the function again w.r.t 'w',
For w=3,
So, it is minimum at w=3.
Now, the dimensions of the box is
Width = 3 ft.
Length = 2(3)= 6 ft
Height =
Therefore, the dimensions of the box that minimize the materials used is