SOLUTION: Claudia works as a manufacturer of decorative jewelry boxes. A customer would like her to create some boxes with the following conditions: The sum of the length and width must b

Question 1151445: Claudia works as a manufacturer of decorative jewelry boxes. A customer would like her to create some boxes with the following conditions:
The sum of the length and width must be 30 centimeters.
The height must be 3 centimeters less than the length.
The box should have the greatest possible volume.
Let's do some math to see if we can decide what size boxes Claudia needs to make, and show what we know about polynomials in the process. Remember: One formula we can use to find the volume of a box is Length * Width * Height.
1. If the length of the box is x, write an expression for the width in terms of x.
2. If the length of the box is x, write an expression for the height in terms of x.
3.What is the maximum volume for the box? Round to the nearest tenth.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of the length and width must be 30 centimeters.
x + w = 30
The height must be 3 centimeters less than the length.
h = x - 3
The box should have the greatest possible volume.
One formula we can use to find the volume of a box is
Vol = Length * Width * Height.
1. If the length of the box is x, write an expression for the width in terms of x.
w = 30 - x
2. If the length of the box is x, write an expression for the height in terms of x.
h = x - 3
3.What is the maximum volume for the box? Round to the nearest tenth.
Vol = length * width * height
V(x) = x * (30-x) * (x-3)
V(x) = x(30x - 90 - x^2 + 3x)
V(x) = x(-x^2 + 33x - 90)
V(x) = -x^3 + 33x^2 - 90x
graphically

3.What is the maximum volume for the box? Round to the nearest tenth.
max occurs when x=21, which is 3400 cu/cm (green)

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