Question

A rectangular box with an open lid is to be made by cutting equal-sked squares of each corner of a 24-inch-by-15-inch piece of cardboard and folding up the resulting a form the sides, as shown in the diagram below. How big should these squares be in o maximize the volume of the box?

Answer 1

V(x) = x(24 - 2x)(15 - 2x)

= x(360 - 78x + 4x²)

= 4x³ - 78x² + 360x

V'(x) = 12x² - 156x + 360 = 0

x² - 13x + 30 = 0

(x - 3)(x - 10) = 0

x = 3 (x = 10 will not work)

These squares should have a side length of 3 cm.