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A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume...

A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 668.25 cubic feet. The cost of wall paint is $0.06 per square foot and the cost of ceiling paint is $0.11 per square foot. Find the room dimensions that result in a minimum cost for the paint by using the method of Lagrange multipliers.

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