Optimization box with maximum volume?

[Sherene]

Homework Statement

A manufacturer wants to design a box having a square base and a surface area of 108m^2. What dimension will produce a box with maximum volume?

Homework Equations

a=x^2+4xy
V=x^2y
a=108m^2

The Attempt at a Solution

 

[clamtrox]

You can use the constraint given for the area to solve either y as a function of x or vice versa. Then you can find the maximum for V(x, y(x)) or V(x(y), y).

 

[MednataMiza]

Another approach is to use the so called Lagrange function or multiplier:
http://mathworld.wolfram.com/LagrangeMultiplier.html

 

[Ray Vickson]

Homework Statement

A manufacturer wants to design a box having a square base and a surface area of 108m^2. What dimension will produce a box with maximum volume?

Homework Equations

a=x^2+4xy
V=x^2y
a=108m^2

The Attempt at a Solution

Is the box open or closed? That affects the surface area.

RGV