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3.4 Linear Programming

3.4 Linear Programming . 10/31/2008. Optimization : . finding the solution that is either a minimum or maximum. Linear Programming. Optimize an “objective function” subject to constraints Graph of constraints is called the “Feasible Region”

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3.4 Linear Programming

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  1. 3.4 Linear Programming 10/31/2008

  2. Optimization: • finding the solution that is either a minimum or maximum

  3. Linear Programming • Optimize an “objective function” subject to constraints • Graph of constraints is called the “Feasible Region” • A minimum or maximum can only occur at a vertex of the feasible region

  4. Example 1 • (ex1) C = - x +3y Objective Function • Find the min/max subject to the following constraints: Step 1:Graph the system of inequalities

  5. Step 2: Find intersections of the boundary lines: List of Vertices: (2,0) , (5,0), (2,8) and (5,2)

  6. Step 3: Test the vertices in the objective function C= -x +3y Minimum Maximum

  7. Example 2 • (ex 2) For the objective function C= x+5y find the minimum and maximum values subject to the following constraints:

  8. Graph System • Graph constraints • Find intersections points: Intersection points (0,2) and (1,4)

  9. Test the vertices in the objective function: Minimum Maximum??? Wait this is smaller???

  10. Closure • Note: If the feasible region is unbounded (open on a side) there may not be a minimum or maximum.

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