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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 A minimum or maximum can only occur at a vertex of the feasible region
Example 1 (ex1)C = - x +3y Objective Function Find the min/max subject to the following constraints: Step 1: Graph the system of inequalitiesGraph
Step 2: Find intersections of the boundary lines: List of Vertices: (2,0), (5,0), (2,8) and (5,2)
Step 3: Test the vertices in the objective function C= -x +3y Minimum Maximum
Example 2 (ex 2) For the objective function C= x+5y find the minimum and maximum values subject to the following constraints:
Graph System Graph constraints Find intersections points: Intersection points (0,2) and (1,4)
Test the vertices in the objective function: Minimum Maximum??? Wait this is smaller???
Closure Note: If the feasible region is unbounded (open on a side) there may not be a minimum or maximum.
Solve the system of inequalities by graphing. x ≤ – 2 y > 3
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