SOLUTION: A closed box is to be constructed from a rectangular sheet of cardboards that measures 18 inches by 42 inches. The box is made by cutting rectangles that measure x inches by 2x inc

Algebra ->  Rectangles -> SOLUTION: A closed box is to be constructed from a rectangular sheet of cardboards that measures 18 inches by 42 inches. The box is made by cutting rectangles that measure x inches by 2x inc      Log On


   

Question 806878: A closed box is to be constructed from a rectangular sheet of cardboards that measures 18 inches by 42 inches. The box is made by cutting rectangles that measure x inches by 2x inches from two of the corners and by cutting two squares that measure x inches by x inches from the top and from the bottom of the rectangle. What value of x (to the nearest thousandth of an inch) will produce a box with maximum volume? Thank you
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
The equation for a box problem will most likely be x(length-2x)(width-2x) unless stated otherwise.
x%2818-2x%29%2842-2x%29
To find the max you plug in numbers for x that are 0%3Cx%3C9.
The reason why you can't use 0 or 9 is because if you plug those numbers into the equation you get out 0. You can't have a volume of 0.
You would usually use a graphing calculator for these problems because it takes forever using a regular calculator.
Your max will be 3.917 with a volume of 1360.497705.