An open top box is to be built with a rectangular base whose length is twice its width and with a volume of 36 ft 3 . Find the dimensions of the box that minimize the materials used.

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

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step-by-step explanation: