Linear Programming: Finding Minimums and Maximums with Constraints

Dec 09, 2025

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This guide explores linear programming techniques to find maximum and minimum values under various constraints. It walks through the process of graphing inequalities to identify the feasible region, shading overlapping areas, and locating corner points. Through practical examples, such as maximizing profit with given constraints or minimizing costs, it illustrates the application of these concepts. Corner points are tested to determine optimum values, where maxima and minima occur. Enhance your understanding of linear programming concepts and their applications in real-world scenarios!

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Linear Programming: Finding Minimums and Maximums with Constraints

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Section 3-4 Linear Programming
Solving for Minimums or Maximums with constraints • Graph the inequalities(CONSTRAINTS) & shade • Identify the overlapping region • Identify the corners of the region • Test the corners to identify the max or min
Maximums & Minimums • If a maximum or minimum exists, they will occur at a corner point.
Example • Given: • Find the point (x,y) that Minimizes C=5x+3y
Example • Given: • Find the point (x,y) that Maximizes P=3x+2y
Example Constraints:
Example Constraints: MAXIMIZE PROFIT: P=60x+40y
Example Constraints: MINIMIZE COST: