Question

Civil Engineering: A rectangular building is being designed that has a volume of exactly 4000[m3]. The walls must be at least 30[m] long and at least 4[m] high. Heat loss is a problem, and the east/west walls lose heat at the rate of 10[energyunits/m2 - day], the north/south walls 8[energyunits/m2 - day], the floor 1[energyunits/m2 - day], and the roof 5[energyunits/m2 - day]. Find the dimensions of the building that minimize heat loss overall.

Answer 1

Let x be the length of the north and south walls, y the length of east and west walls and z the height of the building.

The heat loss is therefore given by h = 10(2yz) + 8(2xz) + 1(xy) + 5(xy) = 6xy + 16xz + 20yz

Since volume is 4000 m^3; xyz = 4000

implies z = 4000/(xy)

the heat loss equation now becomes h(x, y) = 6xy + 80,000 / x + 64,000 / y .