Essay
A closed rectangular container with a square base is to have a volume of 12 cubic metres. The material for the top and bottom of the container will cost $6 per square metre and the material for the sides will cost $4 per square metre. Let x be the length of a side of the base (in metres) and C(x) be the total cost of the container (in dollars). Determine
(a) the total cost C(x).
(b) the dimensions of the most economical box.
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