- 6

- 0

**Optimization, Minima, new question:Sheet Alluminum**

**1. Homework Statement**

A box with a square base and no top must haave a volume of 10000 cm^3. If the smallest dimension in any direction is 5 cm, then determine the dimensions of the box that minimize the amount of material used.

**2. Homework Equations**

Volume: x^2y

Surface Area: x^2+4xy

**3. The Attempt at a Solution**

Let x represent the length and width of the box

Let y represent height

x>5

I drew a neat little drawing of the box and labeled it according to the statements above.

V=x^2y

10000=x^2y

y=10000/x^2

SA=x^2+4xy

=x^2+4x(10000/x^2)

Now I think that I need to set the SA equation to zero then differentiate but I can't quite remember what I'm doing with it. I'd appreciate anyhelp that could be offered.

~Thanks!

Last edited: