A box is to be made from a rectangular piece of cardboard by cutting a square from each corner and folding up the sides. The rectangular piece of cardboard is originally 28 inches long and 54 inches wide, and the squares
Removed from the corners are x inches wide. The volume of the box is given by the function $V = x ( 28 - 2 x ) ( 54 - 2 x )$ What restrictions must be placed on x to satisfy the conditions of this model? In other
Words, what is the domain of this function?

Question

A box is to be made from a rectangular piece of cardboard by cutting a square from each corner and folding up the sides. The rectangular piece of cardboard is originally 28 inches long and 54 inches wide, and the squares
Removed from the corners are x inches wide. The volume of the box is given by the function

V = x ( 28 - 2 x ) ( 54 - 2 x )

What restrictions must be placed on x to satisfy the conditions of this model? In other
Words, what is the domain of this function?

Quizplus · Accepted Answer

The value of x must be positive for the squares to be cut out, but it also must be less than half the length and width of the cardboard to avoid overlapping cuts. Since the cardboard is 28 inches long and 54 inches wide, the maximum value for x is half of 28, which is 14. Therefore, $0 < x < 14$.

A Box Is to Be Made from a Rectangular Piece V=x(28−2x)(54−2x)V = x ( 28 - 2 x ) ( 54 - 2 x )V=x(28−2x)(54−2x)

A Box Is to Be Made from a Rectangular Piece $V = x ( 28 - 2 x ) ( 54 - 2 x )$