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

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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(39838) About Me  (Show Source):
You can put this solution on YOUR website!
x, side length of top and bottom;
y, height of the box;
Total area, 2x%5E2%2B4xy;
Volume, x%5E2%2Ay=25.

The AREA is the function you want to study for its cost.
C%28xANDy%29=1%2A2x%5E2%2B5%2A4xy and x%5E2%2Ay=25.

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 y=25%2Fx%5E2. Substitute,....


C%28x%29=2x%5E2%2B20x%2825%2Fx%5E2%29
highlight%28C%28x%29=2x%5E2%2B500%2Fx%29-----Can you look for the minimum cost using this cost as a function of x?