I'm having problems with optimizing the total surface area of a building to find the minimal dimensions and the equation I came up with is a bit too hard to optimize (I'm a high school student) and I am stuck and don't know what to do. I have provided a link with the image and the variables.
$$ A_{total}=2a+2b+4h+bh_{roof}+2ac $$
As you can see, the equation has 5 variables. I also have an equation for the volume, if that helps: $$ V_{total}=ab\left(h+h_{roof}\over 2\right) $$
I've tried to solve it using a particular volume but that didn't help since there are still many variables. I have heard about the Lagrange method but I don't know very much about it and couldn't use it therefore.
Thanks in advance, your help is very much needed :)