Mathematics

Mathematics

Problem

A company packages candy in a rectangular box with a square base and no internal dividers. The box must have a volume of 216 cm3216\text{ cm}^3. Cardboard for the base costs \0.06persquarecentimeter,whilecardboardforthefoursidesandthetopcosts0.06 per square centimeter, while cardboard for the four sides and the top costs 0.02 per square centimeter. Determine the side length xx (in centimeters) of the square base that minimizes the total material cost of one box.

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