A box with a square base and no top must have a volume of 10 000 cm3. If
the smallest dimension is 5 cm, determine the dimensions of the box that
minimize the amount of material used.

Question

A box with a square base and no top must have a volume of 10 000 cm3. If
the smallest dimension is 5 cm, determine the dimensions of the box that
minimize the amount of material used.

anonymous · Answer

By the way this is an optimization problem.

anonymous · Answer

You need the formula for surface area here. That is S=x^2 + 4xy, so the formula for the volume of this box is (x^2)y=10,000 cm3. Solve for y and you get y=(10000/(x^2)). You can plug this into the original SA equation, so it has a single variable, then set the derivative equal to zero. Plug the number you get into the second derivative and if it is a negative number, than it is a max and if it is positive, then it is a min.

anonymous · Answer

whoa

anonymous · Answer

@lord id listen to the Brain

anonymous · Answer

Thank you =)

anonymous · Answer

I did that. I got an answer. It seems to be wrong. 

And, that way we don't use the information: "Smallest dimension is 5"

anonymous · Answer

I worked out the problem and I got 27.1442 as the minimum. I plugged it into the second derivative and got a positive answer, so it must be a min. as oppose to a max. You may have taken the wrong derivative.

anonymous · Answer

The first derivative I had was: $$2x - 40000/x^{2} =0$$ The second derivative was: $$2 + 40000/x^{3}=0$$

anonymous · Answer

Thank you. That seems to be right.