Linear programming is a method of optimizing a linear objective function subject to linear equality and inequality constraints. It involves representing problems as systems of linear equations and using matrix algebra to solve them. The goal is typically to maximize profits or minimize costs by finding the optimal values of variables. Both the objective function and constraints must be linear, and all parameters must be known with certainty and variables must be non-negative. Common solution methods include the graphical method and simplex method.

1. Linear Programming
Linear programming (LP) problem is to optimize a linear function of several variables subject to linear constraints
an application of matrix algebra used to solve a broad class of problems that can be represented by a system of
linear equations
LP problems are characterized by an objective function that is to be maximized or minimized, subject to a number of
constraints. Both the objective function and the constraints must be formulated in terms of a linear equality or
inequality. Typically; the objective function will be to maximize profits (e.g., contribution margin) or to minimize costs
(e.g., variable costs)..
The following assumptions must be satisfied to justify the use of linear programming:
Linearity. All functions, such as costs, prices, and technological require-ments, must be linear in nature.
Certainty. All parameters are assumed to be known with certainty.
Nonnegativity. Negative values of decision variables are unacceptable.
Two approaches were commonly used to solve LP problems:
Graphical method
Simplex method