Question

A rectangular building is being designed to minimize heat loss. The east and west walls lose heat at a rate of 10 units/m2 per day, the north and south walls at a rate of 8 units/m2 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) Derive a function that describes the heat loss of the building. What is the domain of this function? (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?

          A rectangular building is being designed to minimize heat loss.
The east and west walls lose heat at a rate of 10 units/m2 per day,
the north and south walls at a rate of 8 units/m2 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)
Derive a function that describes the heat loss of the building.
What is the domain of this function? (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?

Added by Julie L.

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