SOLUTION: You are to construct an open box from a rectangular sheet of cardboard that measures 18 inches by 25 inches. To assemble the box, you make the four cuts shown in the figure bel

Question 1139325: You are to construct an open box
from a rectangular sheet of cardboard that measures 18
inches by 25 inches. To assemble the box, you make the four
cuts shown in the figure below and then fold on the dashed
lines. What value of x (to the nearest 0.01 inch) will produce a
box with maximum volume? What is the maximum volume (to
the nearest 0.1 cubic inch)?
Figure: https://i.imgur.com/lPeHsph.png
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
You are to construct an open box from a rectangular sheet of cardboard that measures 18 inches by 25 inches.
To assemble the box, you make the four cuts shown in the figure below and then fold on the dashed lines.
What value of x (to the nearest 0.01 inch) will produce a box with maximum volume?
:
From the diagram we can see the dimensions will be (25-4x) by (18-2x) and the height will be x
the volume then
V = (25-4x)*(18-2x)*x
FOIL
V = (450-50x-72x+8x^2)*x
V = 8x^3 - 122x^2 + 450x
We can plot this

Max volume is when x = 2.41"
RELATED QUESTIONS
[ An open box is constructed from a rectangular sheet of cardboard that measures 12... (answered by TimothyLamb)

An open box is to be made from a piece of cardboard that measures 40 inches on each side. (answered by ikleyn)

A closed box is to be constructed from a rectangular sheet of cardboards that measures 18 (answered by erica65404)

Suppose that an open box is to be made from a square sheet of cardboard by cutting out... (answered by gonzo)

Suppose that an open box is to be made from a square sheet of cardboard by cutting out a... (answered by josgarithmetic)

The area of the rectangular piece of cardboard shown on the left is 198 square inches.... (answered by ankor@dixie-net.com)

The area of the rectangular piece of cardboard shown below is 216 square inches. The... (answered by ankor@dixie-net.com)

The area of the rectangular piece of cardboard shown on the left is 171 square inches.... (answered by alicealc)

Suppose that the open-top box being made from a sheet of cardboard is required to have at (answered by Alan3354)