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.

l = 20.5 cm

h = 17.5 cm

w =  9.5 cm

Step-by-step explanation:

Conditions

l+w =30     Solving for w     30 - l = w

h = l-3

V = l*w*h

Substituting in

V = l * (30-l) * (l-3)

   = (30l-l^2) (l-3)

   = 30 l^2 - l^3 - 90l + 3l^2

Combining like terms

Step-by-step solution

-l^3 + 33 l^2 - 90 l

To find the maximum we need to take the first derivative and then set it equal to zero

-3l^2 + 66l -90 = 0

Factor out a -3

-3 (l^2 -22l +30) =0

Using my calculator and the quadratic formula

l = 11 - sqrt(91)

l = 11 + sqrt(91)

l = 1.5 or 20.5  approximately

If l = 1. then

h= l-3   would be negative  so

l = 20.5

h = l-3

h = 17.5 approximately

w = 30-l = 9.5 approximately

step-by-step explanation:

no of data

divide by no of mode

∞ this is your sign