Acandy box is made from a piece of cardboard that measures 43 by 23 inches. squares of equal size will be cut out of each corner. the sides will then be folded up to form a rectangular box. what size square should be cut from each corner to obtain maximum volume?

For maximum volume of the box, squares with 4.79 inches should be cut off.

Step-by-step explanation:

A candy box is made from a piece of a cardboard that measures 43 × 23 inches.

Let squares of equal size will be cut out of each corner with the measure of x inches.  

Therefore, measures of each side of the candy box will become

Length = (43 - 2x)

Width = (23 - 2x)

Height = x

Now we have to calculate the value of x for which volume of the box should be maximum.

Volume (V) = Length×Width×Height

V = (43 -2x)(23 - 2x)(x)

  = [(43)×(23) - 46x - 86x + 4x²]x

  = [989 - 132x + 4x²]x

  = 4x³- 132x² + 989x

Now we find the derivative of V and equate it to 0

= 0

Now we get values of x by quadratic formula

x = 17.212, 4.79

Now we test it by second derivative test for the maximum volume.

For x = 17.212

This value is > 0 so volume will be minimum.

For x = 4.79

-149.04 < 0, so volume of the box will be maximum.

Therefore, for x = 4.79 inches volume of the box will be maximum.