For problems 1.1-1.8. identify the following problem components:
(a) decision variables;
(b) parameters;
(c) the objective function in words; and
(d) constraints in words.
Geotechnical. The design engineer for a large building must determine the foundation type and size that will ensure that excessive settlement of the building does not occur. Damage costs to the building increase with the degree of settlement. The engineer has some idea of the probability of finding a certain soil strength, but a better estimate can be obtained from field experiments and from laboratory tests. There are many possible experiments available, and generally the reliability of an experimental test result increases with the cost of the test. However, for every test there is still a chance that the test result is not representative of the average soil condition. From past experience and data, the engineer can estimate the probability of having a certain soil strength given a particular experimental result from a particular test. The engineer wants the total expected cost of designing, constructing, and maintaining the building to be minimum—including the costs of soil testing.
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