An open box with a rectangular base is to be constructed from a rectangular piece of cardboard... (details below)

Question

... 18 inches wide and 22 inches long by cutting a square from each corner and then bending up the resulting sides x inches. Define the volume of the box as a function of x. State the domain and sketch the function. Find the value of x that will yield the maximum volume.

Answer 1

Volume = length * width * height

V(x) = (22 - 2x)(18-2x)x

= 4(11-x)(9-x)x

= 4(99-20x + x^2)x

= 4(99x - 20x^2 + x^3)

Max occurs at (3.284, 579.359)