The question as written is
You need to make a closed box with a square base and volume of 32,000 inches cubed . The material for the top and bottom of the box costs \$1 per square inch, and the materials for the sides cost \$0.25 per square inch, Find the dimensions of the box that minimize the cost.
Okay so the problem I'm having here is setting up the equation. The volume of a cube is x^3. The area of a square is x^2. So I should set the price equal to the top and bottom as
\$1(x2) + $1(x2) and I get 2x2. The price for the sides is \$0.25(x2)(4) which just comes to \$1(x2) too. So the cost function should just be 3x2 right? And the derivative is 6x. But if I set that 6x=0 I just get x=0 for the critical point. But that doesn't look right to me. Where did I mess up?