Posted by Jacob on Wednesday, March 13, 2013 at 5:04pm.
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, Wednesday, March 13, 2013 at 5:10pm
we've been through several of these box problems now.
Have you some ideas of how to proceed?

Applied Calculus  Jacob, Wednesday, March 13, 2013 at 5:12pm
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, Wednesday, March 13, 2013 at 5:21pm
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.
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