Applied optimization
i just need to know how to get started.
a rectangular tank that is 6912 ft^3 with a square bbase and open top is to be constructed of sheet ssteel of a given thickness. find the dimensions of the tank with the minimum weight.

Minimum weight => minimum area

Area = area of the base + area of the four sides

Length of the side of the square base: x

area of the base = x^2

area of the other four sides = 4 * x * height

Now you have to put height in therms of x using the volume formula:

Volume = area of the base * height => height = Volume / area of the base

height = 6912 / x^2 => area of the four sides = 4*x*6912 / x^2 = 27648 /x

Total area = x^2 + 27648/x

That is the function that you have to optimize (find the derivative and equal it to zero).

I think this is enough information to you develop the proble,