SOLUTION: pleeeeeeeeeeeeease help me! my assignment is due in 4 hours!!!! a box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in

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Question 230357: pleeeeeeeeeeeeease help me! my assignment is due in 4 hours!!!!
a box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides
a) find a function that models the volume of the box
b) find the values of x for which the volume is greater than 200 in^3
c) find the largest volume that such a box can have.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides
a) find a function that models the volume of the box
Draw the picture of the rectangular piece
Sketch the square corners that are cut out of the rectangle.
Each square has dimensions x by x.
Imagine folding up the sides to form a box.
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The base of the box is (12-2x)by(20-2x) in area
The height of the box is x
The Volume of the box is x(12-2x)(20-2x)
V = x(240-24x-40x+4x^2)
V = 4x^3 - 64x^2 + 240x
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b) find the values of x for which the volume is greater than 200 in^3
Solve 4x^3 - 64x^2 + 240x - 200 > 0
I graphed it and found the x value is greater than 10.928...
But that x-value is not possible since one of the base dimensions
is 20-2x. So no x value gives a volume greater than 200 in^3
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c) find the largest volume that such a box can have.
I'll leave that to you.
Cheers,
Stan H.