SOLUTION: An open crate will be constructed from 12 by 12 (inches) piece of wooden plywood by cutting away squares of equal size from four corners and folding up the sides. Determine the siz

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: An open crate will be constructed from 12 by 12 (inches) piece of wooden plywood by cutting away squares of equal size from four corners and folding up the sides. Determine the siz      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1082919: An open crate will be constructed from 12 by 12 (inches) piece of wooden plywood by cutting away squares of equal size from four corners and folding up the sides. Determine the size of the cutout that maximizes the volume of the box. Find the length, width, and volume of the crate.
Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
v for the volume:
x, the size of edge length of the cutout corner

v=x%2812-2x%29%2812-2x%29
-
v=x%28144-48x%2B4x%5E2%29
v=4x%5E3-48x%5E2%2B144x


dv%2Fdx=12x%5E2-96x%2B144=0
3x%5E2-24x%2B36=0

discriminant, 24%5E2-4%2A3%2A36=144=12%5E2

x=%2824%2B-+12%29%2F6
system%28cross%28x=6%29%2Cor%2Chighlight%28x=2%29%29

Length and width each is 8 inches.
Volume is 128 cubic inches.