calculus word problem

Question

A box​ (with no​ top) will be made by cutting squares of equal size out

of the corners of a 31 inch by 60 inch rectangular piece of​ cardboard,

then folding the side flaps up. Find the maximum volume of such a box.

ROUND TO THE NEAREST CUBIC

INCH.

The maximum volume is ___

cubic inches.

Answer 1

Let x = length of a side of a square

V = x(31 - 2x)(60 - 2x) = 4x³ - 182x² + 1860x

V' = 0 Solve for x.