Optimization, Minima, new question:Sheet Alluminum 1. The problem statement, all variables and given/known data 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. Relevant 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!