SOLUTION: I really need help with this problem, I'd appreciate a detailed explanation too because it's really important!!! You have a flat sheet of cardboard that is 10 inches long and 8

Question 1174860: I really need help with this problem, I'd appreciate a detailed explanation too because it's really important!!!
You have a flat sheet of cardboard that is 10 inches long and 8 inches wide. You need to make a box that has the maximum area. So you decide to cut out square corners of the sheet of cardboard, and fold the cardboard to make a box. Let x represent the side of each little square you cut out. Write a function for the area of the box and use your graphing calculator to graph it.
What is the maximum area of your box, and what value of x gives you that maximum area? Be sure to justify your answer.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
You have a flat sheet of cardboard that is 10 inches long and 8 inches wide.
You need to make a box that has the maximum volume.
So you decide to cut out square corners of the sheet of cardboard, and fold the cardboard to make a box.
Let x represent the side of each little square you cut out.
Write a function for the volume of the box and use your graphing calculator to graph it.
What is the maximum volume of your box, and what value of x gives you that maximum area?
Be sure to justify your answer.
:
the dimensions of the box will be
(10-2x) by (8-2x) by x, which is the height
f(x) = Volume
V = (10-2x)*(8-2x)*x
FOIL
v = (80-20x-16x+4x^2)*x
V = (80-36x+ 4x^2)*x
multiply by x, arrange in the standard order
V = 4x^3 - 36x^2 = 80x
Graph this equation, volume is on the vertical axis, x is the horizontal

calc shows max volume is when x = 1.47 inches and
then the max vol = 52.5 cu/in (green line)
:
You can confirms this by replacing 1.47 for x in the original equation, and finding the volume
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