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.
we've been through several of these box problems now.
Have you some ideas of how to proceed?
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.
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.