# Calculus

A carpenter wants to make an open-topped box out of a rectangular sheet of tin 24 inches wide and 45 inches long. The carpenter plans to cut congruent squares out of each corner of the sheet and then bend the edges of the sheet upward to form the sides of the box. If the box is to have greatest possible volume, what should its dimensions be?

1. If the cuts are length x, then the volume is

v = (24-2x)(45-2x)(x)
= 4x^3 - 138x^2 + 1080x

dv/dx = 12x^2 - 276x + 1080
= 12(x^2-23x+90)
= 12(x-18)(x-5)

You can take it from there ...

posted by Steve

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