Optimization w/ Surface Area

I am given the dimensions of a box (h=14,w=10,l=3) I have to preserve the ratio of H:W, which is 7:5. L does't need to be porportional to anything. I am told I must maintain the H:W ratio and the volume. The volume I found to be 420 in.^3.

The surface area equation is 2lw+2lh+2wh

I need to minimize the amount of surface area on the box while maintaining the specified factors including the volume.

I have tried many things including replacing lw, lh, wh, none have worked. Can someone please show me how to do this, I need to find:

- Equation of SA(l) where SA(l)=aL^2+b/L^c
- The minima

If someone can please show me how to do it?

Re: Optimization w/ Surface Area