Study Notes
Linear programming involves deriving linear inequalities and finding regions in a plane to determine the greatest and least values for an inequality. It uses the Cartesian plane, where two real number lines intersect perpendicularly, to represent data as points and inequalities as regions.
- Linear Inequality — An inequality that represents an interval or range following a linear condition. Example: 3x + y ≥ 1 represents a region on the Cartesian plane.
- Cartesian Plane — A two-dimensional plane formed by two perpendicular axes. Example: The x-axis and y-axis intersecting at the origin.
- Region — A part of the plane that satisfies a set of inequalities. Example: The shaded area above the line 3x + y = 1.
Exam Tips
Key Definitions to Remember
- Linear Inequality: An inequality involving a linear expression.
- Cartesian Plane: A plane with two perpendicular axes.
Common Confusions
- Confusing the solution region with the unwanted region.
- Misinterpreting the inequality symbols when shading regions.
Typical Exam Questions
- What is the inequality for at least 100 biscuits? x ≥ 100
- How do you represent a maximum of 300 items? x + y ≤ 300
- How do you find the maximum profit? Use the objective function with the feasible region.
What Examiners Usually Test
- Ability to derive and graph inequalities.
- Identifying and shading the correct region on the graph.
- Calculating maximum or minimum values using the objective function.