Definitions [5]
Definition: Solution Set of a System
The common region satisfying all the given inequalities is called the solution set.
Definition: Optimize
To optimise means to maximise or minimise.
Definition: Convex Region
A region is said to be convex if the line segment joining any two points in the region lies entirely within the region.
Definition: Objective Function
The linear function whose maximum or minimum value is to be determined is called the objective function.
Definition: Standard Forms of Linear Inequalities
The equation ax + by = c is called the associated equation of the inequality.
Theorems and Laws [1]
Theorem: Fundamental Theorem of Linear Programming
Statement:
If a linear objective function has a maximum or minimum value over a feasible region, then the maximum or minimum occurs at one of the corner points of the feasible region.
Key Points
Key Points: Region representation
| Condition | Region represented |
|---|---|
| ( x > 0 ) | Right of the y-axis |
| ( x < 0 ) | Left of the y-axis |
| ( y > 0 ) | Above x-axis |
| ( y < 0 ) | Below x-axis |
| ( x ≥ 0 ) | Includes y-axis |
| ( y ≥ 0 ) | Includes x-axis |
