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Section 8.5 Linear Programming

Subsection 1. Use new vocabulary

Subsubsection Definitions

Write a definition or description for each term:

  1. Objective function
  2. Constraint
  3. Feasible solution
  4. Optimum solution
  5. Vertex

Subsubsection Exercise

Illustrate each term above for the TrailGear example at the start of Section 8.5

Answer
  • The objective function is \(~P-8x+10y.\)
  • The constraints are \(~3x+6y \le 2400~\) and \(~2x+y \le 1000.\)
  • The feasible solutions are all the solutions to the inequalities in the constraints.
  • The optimum solution is \((400, 200)\text{,}\) which is one of the vertices of the set of feasible solutions, that is, an intersection point of the boundary lines of that set.