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3.3 Linear Programming

Learn how to use linear programming to maximize profit by graphing constraints, shading feasible regions, and identifying intersection points to optimize your objective function. Practice problems included.

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3.3 Linear Programming

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  1. 3.3 Linear Programming

  2. Vocabulary • Constraints: linear inequalities; boundary lines • Objective Function: Equation in standard form used to determine the maximum or minimum value of the graph. • The process of maximizing or minimizing the objective function is called linear programming. • Feasible region: the intersections of the graph. : the common shaded area.

  3. Use Linear Programming to Maximize the Profit • (EX 1) Constraints: x ≥ 4 y ≤ 0 5x + 4y ≤ 40 Objective Function: P = 35x + 30y Steps: • Graph the constraints • Shade the feasible region • Label the ordered pairs that are the intersections of the feasible region. • Use the ordered pairs to substitute into the objective function to determine the maximum and minimum value.

  4. Checking Vertices • Practice Problems: Page 176 (1-6)

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