A rectangular storage container with an open top is to have a volume of 45m^3. the length of its base its base is twice its width. Material for the base costs $5 per square meter and meterial for the sides costs $4 per square meter. Find the cost for the cheapest such container.

Question

zepdrix · Answer

Hmm this one is almost exactly like the last one :D still having trouble with these yashar?

anonymous · Answer

yes` I don;t know how to use those costs?

anonymous · Answer

Also total cost?

zepdrix · Answer

Oh i see, this is actually the opposite of the last one we did.

Here, Volume is our constraint. We have a fixed volume, and we want to know what dimensions would make it the least expensive to build.

So in this problem, we'll want to differentiate cost.
What is cost referring to though?
It's a cost per SQUARE meter, that applies to SURFACE AREA.

So we need an equation for Surface Area of a box with an OPEN top.

zepdrix · Answer

The length of it's base is twice it's width. Lemme try to draw that again :3 my bad.

anonymous · Answer

ok

zepdrix · Answer

|dw:1353564266646:dw|
So these should be the dimensions for the box. Understand where those are coming from? :D

anonymous · Answer

why is it 2x ?

zepdrix · Answer

If we label the WIDTH as x, some unknown quantity, then the LENGTH is twice that long -based on what the problem told us.

anonymous · Answer

ok got it