Hi there, I got a school problem that I need solving, I don't want to get the answer but I would love to get pointer as to where I have done something wrong.
The problem is as following:
I got a box with a lid on top. The base area is X*X and the height is H. H is the box + the extra height of the lid.
The lid has the size of the base area + 4 side plates that are 3 cm high.
The conditions are that the box should be 1000kubic cm large and the material needed should be as little as possible.
I figured that if I am to decide what the least amount of materials needed I need to set up a function and I have decided to calculate the Area of materials as a function of X.
With the conditions that X^2*(H-3)=1000 I get that H=1000/X^2+3
Total amount of materials f(X)=2X^2+4HX F(X)=2X^2+4*(1000*X^-2+3)X
And by derivation I should find the dimensions that gives us the least materials used. It feels wrong but I don't know what it is. So if you see any direct errors in the math please tell me and any pointers or hints as to how I should proceed would be greatly appreciated.