1. The problem statement, all variables and given/known data A rectangular building is being designed to minimize heat loss. The east and west walls lose heat at a rate of 10 units/m^2 per day, the north and south walls at a rate of 8 units/m^2 per day, the floor at a rate of 1 unit/m^2 per day, and the roof at a rate of 5 units/m^2 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 m^3. Find the dimensions that minimize heat loss. (check the critical pts and boundary pts) 3. The attempt at a solution Since Length x Width=120, the height must be 33 1/3 m. I'm having trouble starting with the equation for heat loss. I so far I have 2(10)x + 2(8)y + (5+1)z. I'm not sure about the z part. The floor loses by a factor of 1, and the roof by a factor of 5. Since they both must have equal area, I figured they must lose at the same rate--that's why I added the 2 numbers together. Can anyone explain it better?