A box with a square base and ope top must have a volume of 32000cm^3. find the dimensions of the box that minimize the amount of material t be used.

Question

anonymous · Answer

If you let "x" be the measure of a side for the base:

V = 32000 = hx^2      ->      h = 32000x^(-2)

The surface area for the open-top box is x^2 + 4hx    ->    

SA = x^2 + 4x[32000x^(-2)] = x^2 + 128000/x

So you can take the first derivative of SA with respect to "x" as it is now an equation with one independent variable.