### Optimization Problems

Find to     Minimize

Subject to and .

#### Building design example

To save energy costs for heating and cooling an architect is considering designing a partially buried rectangular building. The total floor space needed is . Lot size limits the building plan dimension to . It has already been decided that the ratio between the plan dimensions must be equal to the golden ratio (1.618) and that each story must be high. The heating and cooling costs are estimated at of the exposed surface area of the building. The owner has specified that the annual energy costs should not exceed . Determining building dimensions to minimize cost of excavation.

Optimization variables

n = Number of stories
d = Depth of building below ground
h = Height of building above ground
ö½ = Length of building in plan
w = Width of building in plan

Objective function

Minimize excavation cost

Constraints

Number of stories related to the building height

Plan dimensions

Floor space requirement

Lot size

Energy cost

Physical limitations

The complete optimization problem can be stated as follows.

Find in order to

Minimize

Subject to