54. A rectangular building is being designed to minimize heat loss. The east and west walls lose heat at a rate of 10 units/m? per day, the north and south walls at a rate of 8 units/m per day, the floor at a rate of 1 unit/m² per day, and the roof at a rate of 5 units/m² 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.

Refrigeration and Air Conditioning Technology (MindTap Course List)
8th Edition
ISBN:9781305578296
Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Chapter33: Hydronic Heat
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54. A rectangular building is being designed to minimize
heat loss. The east and west walls lose heat at a rate of
10 units/m? per day, the north and south walls at a rate of
8 units/m? per day, the floor at a rate of 1 unit/m²
and the roof at a rate of 5 units/m² 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
per day,
of the lengths of the sides.
Transcribed Image Text:54. A rectangular building is being designed to minimize heat loss. The east and west walls lose heat at a rate of 10 units/m? per day, the north and south walls at a rate of 8 units/m? per day, the floor at a rate of 1 unit/m² and the roof at a rate of 5 units/m² 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 per day, 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?
Transcribed Image Text:(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?
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