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Solving Linear Inequalities with Convex Polygons: Visualization and Optimization

Learn to solve systems of linear inequalities graphically, utilizing polygonal convex sets and the vertex theorem. Apply techniques to find maximum and minimum values for the given multivariable function within the specified constraints.

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Solving Linear Inequalities with Convex Polygons: Visualization and Optimization

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  1. 2-6 Solving Systems of Linear Inequalities Pre Calc A

  2. Vocabulary • Polygonal convex set • Vertex theorem • System of linear inequalities

  3. Ex 16 + 1: • Review • Graph x + 2y ≥4 X – y ≤ 3

  4. Ex 17: • Solve the system of inequalities by graphing • x≥0 • y≥0 • X + y ≤ 5

  5. Ex last one: • Find the minimum and maximum values of f(x,y)= y – 2x + 5 for the polygonal convex set determined by the system of inequalities. • x≥1 • y≤8 • 2x + y≤14 • y≥2 • X + y ≥5

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