Question: A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 458 in. The cost of

A company plans to manufacture a rectangular box with a square base,

A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 458 in. The cost of the material for the base is 0.5 cents per square inch, and the cost of the material for the sides is 0.4 cents per square inch. Determine the dimensions of the box that will minimize the cost of manufacturing it. What is the minimum cost per box rounded to the nearest cent? Round any calculations and the final answer to the nearest hundredth if necessary.

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