Linear Programming. What is linear programming? Use a system of constraints (inequalities) to find the vertices of the feasible region (overlapping shaded.

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Presentation transcript:

Linear Programming

What is linear programming? Use a system of constraints (inequalities) to find the vertices of the feasible region (overlapping shaded region) Use a system of constraints (inequalities) to find the vertices of the feasible region (overlapping shaded region) Use the vertices to find the maximum and/or minimum value for a given function Use the vertices to find the maximum and/or minimum value for a given function

Find the feasible region Constraints Graph the lines Points of intersection (3, 5) (-5, -3) (1, 9)

Find the Maximum and Minimum values The function Plug each point into the function Maximum Minimum

Word Problems There are a total of 85 work hours available per day for production at a calculator manufacturer. There are 60 workers’ hours available for encasement and quality control each day. The following system represents the number of calculators that can be produced. Let x represent the number of graphing calculators and let y represent the number of CAS calculators.

Use the function to find the maximum profit Function Vertices (0, 0) (30, 0) (0, 85) (14, 64) Maximum profit of $5525 occurs when 0 graphing calculators are produced and 85 CAS calculators are produced