# calculus

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A box is contructed out of two different types of metal. The metal for the top and bottom, which are both square, costs \$5 per square foot and the metal for the sides costs \$2 per square foot. Find the dimensions that minimize cost if the box has a volume of 40 cubic feet.

• calculus -

So, the height is 40/x^2

c(x) = 2x^2*5 + 4x(40/x^2)*2
= 10x^2 + 320/x

set the derivative to zero, and you find minimum cost at x = 2∛2

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