SOLUTION: A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $1 per square foot and the metal for the sides costs $5 per

Question 1001621: A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $1 per square foot and the metal for the sides costs $5 per square foot. Find the dimensions that minimize cost if the box has a volume of 25 cubic feet.
Thanks to whoever helps!
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
x, side length of top and bottom;
y, height of the box;
Total area, ;
Volume, .

The AREA is the function you want to study for its cost.
and .

You want to make C(x) OR C(y), and you use the volume relationship to do this. You can find the minimum cost from there. Best might be to start with . Substitute,....

-----Can you look for the minimum cost using this cost as a function of x?
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