A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions length=9 ft

A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions length=9 ft and width=6 ft by cutting a square piece out of each corner and turning the sides up as shown in the picture.

Determine the length x of each side of the square that should be cut which would maximize the volume of the box.

Expert Solution

Taking the derivative of the volume with respect to x

Hence the length x will be equal to 5/2 - sqrt(7)/2 which will maximize the volume

So, x = 1.177

milcah answered 2 years ago

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