Optimization Problems (Quick Question)
I'm on my way to solving this problem, I just need a little help.
"The volume of a square-based rectangular cardboard box is to be 1000cm^3. Find the dimensions so that the quantity of material used to manufacture all 6 faces is a minimum. Assume that there will be no waste material. The machinery available cannot fabricate material smaller in length than 2cm."
Knowing that it is a square-based shape, you can assume that length = width = height. Therefore, V = x^3. Easy.
The volume of the cardboard box has to be 1000cm^3.
Therefore, 1000cm^3 = x^3. The domain in this problem is 2 < x < ____.
I don't know where to go from here, could someone provide some insight?
How do I figure out the maximum end point for the domain, and what would my next step be?