Yet another optimization problem... if anyone knows how to solve this please explain it to me:

Thank you.A box with a square base and open top must have a volume of 32,000cm3. Find the dimensions of the box that minimize the amount of material used.

Set up an equation for the amount of material used as a function of one of the dimensions of the box. If H is the height and L the dimension of the square base, then you know that:

32000 = HL^2

The area of material used is the sum of the areas of the four sides plus the top & bottom: A = 4HL + 2*L^2.

You can combine these to get an equation that gives A as a function of L. Then use the technique I described in response to the other question you posted to solve for the value for L that gives a minimum value for A.

You must minimize the surface area given the volume is

Since there is no top, the surface area is given by

Solve the volume equation for, say, y; Sub it into S; differentiate, set to 0 and solve for x.

The y value will then follow.