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  3. Chapter 5: Optimization
  4. Optimization constrained extremum problems
  5. First-order condition constrained extremum problem

First-order condition constrained extremum problem

Introduction: A constrained extremum problem is given by
  • Optimize z(x,y)
  • Subject to g(x,y)=k
  • Where x∈D1, y∈D2
Theorem: An extremum location (c,d), where c∈D1 and d∈D2 that is not a boundary point, satisfies the following system of equations:
  • z′x(x,y)z′y(x,y)=g′x(x,y)g′y(x,y)
  • g(x,y)=k

Remark: Do not forget to check whether the extremum is a minimum or a maximum.