Maximizing Volume: Finding Optimal Dimensions for a Box with an Open Top

[justin345]

Homework Statement

A box with a square base is to have an open top. The area of the material in the box is 60 sr in. What are the dimensions when the volume is maximized?

Homework Equations

The Attempt at a Solution

A=x²+4xy
V=x²y

x²+4xy=60
4xy=60-x²
y=(60-x²)/4x

Where do I go from here?

 

[hgfalling]

Have you done this kind of maximization problem before? You want to get an function for volume in terms of a single variable (which you are about to do). Then you differentiate the function and set the derivative equal to zero.