Linear Programming

Linear Programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model. Its function and constraints are linear.

The objective function represents the goal of the linear programming problem, typically to maximize or minimize a certain quantity, such as profit or cost.

Constraints are the restrictions or limitations on the variables in a linear programming problem, often expressed as inequalities.

The feasible region is the set of all possible points that satisfy the constraints of a linear programming problem, typically represented graphically.

To maximize an objective function means to find the highest possible value of that function within the feasible region.

To minimize an objective function means to find the lowest possible value of that function within the feasible region.

The graphical method is a way to solve linear programming problems by plotting the constraints on a graph and identifying the feasible region.

Corner points (or vertices) of the feasible region are significant because the optimal solution to a linear programming problem will occur at one of these points.

A constraint can be represented mathematically as an inequality or an equation, such as $$x + y \leq 8$$ .

The standard form of a linear programming problem is to maximize or minimize an objective function subject to linear equality and non-negativity constraints.