Applications to oil industry problems of several mathematical techniques related to maximization or minimization are surveyed. In addition to providing an extensive, although not exhaustive, coverage of the relevant papers and books, the report may serve as an elementary introduction to the topics involved. To further this goal, simple illustrations of the central ideas are given. These include new examples as well as simplified versions of old ones. Finally, an attempt is made to evaluate the limitations and potential utility of some of the techniques. Management Technology, ISSN 0542-4917, was published as a separate journal from 1960 to 1964. In 1965 it was merged into Management Science.