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A company wants to manufacture a rectangular planter box of volume 12 litres (12, 000 cm3...

A company wants to manufacture a rectangular planter box of volume 12 litres (12, 000 cm3 ). The box is open at the top and is designed to have its width equal to half of its length. The plastic used for the base of the box is stronger and costs 0.06 cents per cm2 while the plastic used for the sides of the box costs 0.04 cents per cm2. Find the length, width and height of the box for which the box has minimum cost. What is the minimum cost? Show all the reasoning and evaluate your answers to 2 decimal places.

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