Help Please! (:

A box with a square top and bottom and volume 20 cubic feet is to be constructed from two different materials. Exotic hardwood coasting 5 dollars per feet squared will be used for the top and bottom. Find the dimensions of the box that minimizes the cost of the materials.

Question

Help Please! (:

A box with a square top and bottom and volume 20 cubic feet is to be constructed from two different materials. Exotic hardwood coasting 5 dollars per feet squared will be used for the top and bottom. Find the dimensions of the box that minimizes the cost of the materials.

zepdrix · Answer

Since the base is square, two of the dimensions we can label the same:
$$\Large\sf V=x\cdot x\cdot  y$$They told us the volume is 20 cubic feet,$$\Large\sf 20=x^2 y$$

And then we have this cost per square feet....
and we need to minimize cost.. hmmmm
I'm having trouble coming up with another equation.. grr

anonymous · Answer

Wouldn't we have to take the derivative of the volume formula of a rectangle/cube? @zepdrix

zepdrix · Answer

The derivative of volume will give us a formula for surface area.
But that's the surface area of the entire cube.
We only want the surface area of the top and bottom right?

I dunno.. this question is really confusing..

zepdrix · Answer

It just doesn't make sense...

If we're trying to minimize cost, we would just make the top and bottom as tiny as possible because they didn't give us a price for the sides.

anonymous · Answer

how would we set this up? right sum? left sum? @zepdrix

zepdrix · Answer

I don't know :(
I don't understand this problem..

anonymous · Answer

@Loser66 @mathstudent55  Help?