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Suppose that you are to make a rectangular box with a square base [B]from two different materials.

Suppose that you are to make a rectangular box with a square base [B]from two different materials.
The material for the top and four sides of the box costs $1/ft^2; the material for the base costs $2/ft^2.
Find the dimensions of the box of greatest possible volume if you are allowed to spend $144 for the
material to make it.

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