Answer: A rectangular building is being designed to minimize heat loss. The east and
Chapter 14, Problem 52(choose chapter or problem)
A rectangular building is being designed to minimize heat loss. The east and west walls lose heat at a rate of per day, the north and south walls at a rate of per day, the floor at a rate of per day, and the roof at a rate of per day. Each wall must be at least 30 m long, the height must be at least 4 m, and the volume must be exactly . (a) Find and sketch the domain of the heat loss as a function of the lengths of the sides.(b) Find the dimensions that minimize heat loss. (Check boththe critical points and the points on the boundary of thedomain.)(c) Could you design a building with even less heat lossif the restrictions on the lengths of the walls were removed?
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