# Pretty simple optimization problem

A closed box with a square base is to contain 252ft^3. The bottom costs 5$per ft.^2, the top is 2$ft^2 and the sides cost 3\$ft^2. Find the dimensions that will minimize the cost.

As for equations we have v=lwh and I'm not sure as to how to find the next relative equation.

I just need to find another formula so I can derive and solve. Any help is much appreciated.
Thankss

What are the areas of the different sections?

What are the areas of the different sections?

It doesnt say, thats directly quoted from the text.
i wanna say its something like
3(lw)=sides 5(lw)-bottom 2(lw)-top

That was meant to be a hint for your next equation. Calculate the areas and you can work out the cost from that. Note that there are only two free parameters since the bottom is a square.