We want to construct a right prism (a 3 dimensional rectangular box) which doesn't have a cap. The material in which is constructed its base costs 5 times the material its walls are made of. (cost is per unit of area).

I have to find the dimensions of the right prism that minimize its cost, considering that its volume must be V.

My attempt : I've the constraint . I'm not really sure about the function I have to minimize. I've thought about since the price of an area unit of times the area unit of and .

So I'd have to work out the critical points of but I found a contradiction by doing so ( ).

So I know I made an error by chosing the function . I'd like a bit of help to chose the right function to minimize. Thanks in advance.