# Pretty simple optimization problem

1. May 10, 2009

### 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

2. May 10, 2009

### phsopher

What are the areas of the different sections?

3. May 10, 2009

### wapakalypse

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

4. May 10, 2009

### 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.