# Solving a word problem using derivatives to find the minimum

I need help solving this equation. Can anyone help?

Find the least amount of material needed to make a square-based open box that has volume of 4000 cubic meters.

-
You have posted ten problems in the last few hours, all covering pretty much the same ground. STOP IT! Instead, read the answers to one question, think about them, try to understand them, see whether you can apply what you learn from one question to the solution of the others. Are you just harvesting answers, or are you actually trying to learn something? –  Gerry Myerson Jun 11 '12 at 7:19

Again, draw a picture. Suppose it is $y$ tall, with base side length $x$. The area of the base is $x^2$, and the sides have area $xy$, so the total amount of material is $x^2+4xy$. The volume is $4000=x^2y$, which you can solve for $y$ to get an expression for total amount of material in terms of $x$. Then it is just like the other problems.
Based on the volume equation, what is $y$? –  Cameron Buie Jun 11 '12 at 4:51
Once you've found that, plug that into the expression for total amount of material, and you'll have a formula with just $x$'s in it, which you can minimize just as with other problems you've posted. –  Cameron Buie Jun 11 '12 at 4:58