DERIVATIVE APPLICATIONS

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JOSH BAR

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Sep 29, 2009
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An open rectangular box with a square base is to be made from 48ft^2 of material. What dimensions will result in a box with the largest possible volume? What is the largest possible volume?

I dont know where to start, I know I have to find a constraint but I am quite lost, HELP!!!!!!!!!
 
JOSH BAR said:
An open rectangular box with a square base is to be made from 48ft^2 of material. What dimensions will result in a box with the largest possible volume? What is the largest possible volume?

I dont know where to start, I know I have to find a constraint but I am quite lost, HELP!!!!!!!!!
Click to expand...

Start with a sketch of the situation and defining variables.

Let the

Length of the box = L

Width of the box = W

Depth of the box = D

Then surface area S = 2* (L*D + W*D) + L*W

The Volume of the box V = L * W * D

Now continue...

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
I am still lost, if I put them as XYZ how would I solve it? I know the area is the constraint, but how do I set it up to start solving for one variable.
 
JOSH BAR said:
I am still lost, if I put them as XYZ how would I solve it? I know the area is the constraint, but how do I set it up to start solving for one variable.
Click to expand...

What is the condition for maximizing/minimizing a function?
 
JOSH BAR said:
Well I am not sure how to even set this problem up or where to begin.
Click to expand...

\(\displaystyle \frac{dF}{dx} \ \ = \ \ 0\)
 
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