1. 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 roof and a rate of 5 units/m2 per day. Each wall must be at least 30m long, the height must be at least 4m, and the volume must be exactly 4000 m3.
A. Construct and sketch the domain of the heat loss as a function of the lengths of the sides
B. Determine the dimensions that minimize the heat loss.