3.1.4 Linear Programming Key Objectives • Write constraints and graph feasible regions. • Use linear programming to answer real-world questions. Key Terms • Linear programming is a method of finding a maximum or minimum value of a function that satisfies a given set of conditions (inequalities) called constraints . • A feasible region is the set of points that satisfies the constraints in a linear-programming problem. • An objective function is the function to be maximized or minimized in a linear-programming problem. Example 1 Graphing a Feasible Region Constraints are the linear inequalities that describe the conditions for a linear programming problem. The graph of the constraints (a system of linear inequalities), called the feasible region, contains all of the possible solutions to the linear programming problem. To write the constraints, first identify the two variables x and y . Note that two of the constraints will be x ≥ 0 and y ≥ 0 when the variables represent unknowns that cannot be negative.
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