Posted by Jacob on .
A rectangular box is to have a square base and a volume of 50 ft3. The material for the base costs 32¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 26¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.

Applied Calculus 
Steve,
we've been through several of these box problems now.
Have you some ideas of how to proceed? 
Applied Calculus 
Jacob,
I had to miss my last week of Calculus due to some personal things, so I had not been through any lectures of optimization. It hurt me greatly, now I have a few of these that I don't know how to set up at all.

Applied Calculus 
Steve,
base is side x, height is h, so
hx^2 = 50
h = 50/x^2
cost of the box is
cost of sides + cost of bottom + cost of top
that should get you started.