An open-top box with a square base must hold of volume

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

An open-top box with a square base must hold 16,000 cm316{,}000\,\text{cm}^3 of volume. The base material costs 0.200.20 dollars per cm2\text{cm}^2, while the material for the four sides costs 0.050.05 dollars per cm2\text{cm}^2. Determine the length of the base, in centimetres, that minimises the total material cost.

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