Question

Help Please! (:
A box with a square top and bottom and volume 20 cubic feet is to be constructed from two different materials. Exotic hardwood coasting 5 dollars per feet squared will be used for the top and bottom. Find the dimensions of the box that minimizes the cost of the materials.

Answer 1

Note that this problem statement does NOT say that the box is a cube, but rather that the top and bottom are both squares.

I'd suggest you start by drawing a diagram showing these square top and bottom, with sides. Label everything: each side of the top and bottom should be labeled, and each side also. Write a formula for the SURFACE AREA of the entire box, using the variables you have chosen (only TWO variables).

Now, your problem statement says that the exotic wood is $5/(ft^2), but it doesn't say how much the common material used to construct the sides is (that is, how much it costs). Wasn't that info given? If not, assume that the material used for the sides is $1/(ft^2).

You'll need to come up with a formula for the total COST of the material.

I will be offline for a while, but will answer later if you haven't already finished this problem by then.