Pretty simple optimization problem

[wapakalypse]

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

 

[phsopher]

What are the areas of the different sections?

 

[wapakalypse]

What are the areas of the different sections?

It doesn't say, that's directly quoted from the text.
i want to say its something like
3(lw)=sides 5(lw)-bottom 2(lw)-top

 

[phsopher]

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.