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A rectangular box is to have a volume of 20 cubic metres. The mate-rial used for...

A rectangular box is to have a volume of 20 cubic metres. The mate-rial used for the sides costs $1 per square metre, the material for thebottom costs $2 per square metre, and the material for the top costs$3 per square metre. What are the dimensions of the cheapest box? Using Multivariable Calculus/Second Derivative Test/Hessian Matrix xyz=20

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