A partially buried, rectangular office building is to be constructed with a volume of at least 50,000 cubic meters. To minimize energy for heating and cooling, the exterior roof and sidewall surface exposed above ground should not exceed 2250 square meters. Within these limits, the designer wishes to choose dimensions that minimize the volume excavated for the buried part of the building.

(a) Formulate this design problem as a constrained NLP.

(b) Use class optimization software to start from a feasible solution and compute at least a local optimum.