Extremum problems

  • Adi Ben-Israel
  • Robert Gilbert
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)


The following example is an illustration of the problems studied in this chapter. Example 6.1. You are the president of the XYZ Widget Company, which is in the business of producing and selling widgets. You must decide how many widgets, say x, to produce in the coming season. The information available to you is:
  • the company can produce no more than 10 000 widgets,

  • the company can sell any quantity it produces at the price of p : = 9 [$/widget],

  • there is a fixed cost of 6 000 [$] (a cost such as rent, which does not depend on the decision x),

  • the variable cost of producing x widgets is 2x + 0.001 x2 [$].

As president your job is to maximize the profit, which is revenue minus costs.


Local Minimum Stationary Point Convex Function Global Minimizer Extremum Problem 
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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Adi Ben-Israel
    • 1
  • Robert Gilbert
    • 2
  1. 1.Rutgers Center for Operations Research and Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Department of Mathematical Science and Computer and Informational SciencesUniversity of DelawareNewarkUSA

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