Box Problem for Alg 2

Question

A box is to be made from a piece of cardboard which measures 20 inches by 24 inches. The box will be formed by cutting out each corner and folding up the sides. What size cut should be made to maximize the volume of the box?

Answer 1

x represents the side of the square cut out

V = x(24 - 2x)(20 - 2x)

V = x(480 - 88x + 4x²)

V = 4x³ - 88x² + 480x

Using the first derivative, the local maximum is at an irrational number.

Review the data.