Solution: A rectangular building is being designed to minimize heat loss. The east and

Chapter 9, Problem 38

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A rectangular building is being designed to minimize heat loss. The east and west walls lose heat at a rate of 10 unitsym2 per day, the north and south walls at a rate of 8 unitsym2 per day, the floor at a rate of 1 unitym2 per day, and the roof at a rate of 5 unitsym2 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 4000 m3 . (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 both the critical points and the points on the boundary of the domain.) (c) Could you design a building with even less heat loss if the restrictions on the lengths of the walls were removed?