Chapter 3: Section 4 Notes
By the end of the section, you should be able to:
- Use linear programming to find the maximum or minimum value of a feasible region of solutions
Definitions:
- Constraint: a value or situation that limits the solution of a problem.
- Linear Programming: a method of finding minimum or maximum value of some quantity, given a set of constraints.
- Feasible Region: The shaded region of the graph that contains all of the points that satisfy all of the constraints.
- This region is the multi-shaded region that satisfies all of the linear inequalities.
- Vertex/Vertices: A point or several points two or more boundary lines of the feasible region meet.
- Ex. If the boundary lines were fences, a vertex would be a ‘corner’ fence post
- Objective Function: The equation that models the quantity that is being minimized or maximized
- often this value is for (minimizing) cost or (maximizing) profit
- If there is a minimum or maximum value of the objective function, it occurs at one or more vertices of the feasible region.
Things/Steps to remember for using Linear Programming/Optimization:
- Graph all of the linear inequalites on one graph to locate the feasible region.
- Write down the coordinates of each vertex point.
- Evaluate the Objective Function for each of the verticies.
- Look for the Maximum/Minimum value of the Objective Function.
Section 3.4 Worksheet |
Section 3.4 WS Answers |
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