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

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) (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.

To find the max you plug in numbers for x that are .
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.
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