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Linear programming (LP) is an application of matrix algebra used to solve a broad class of problems that can be represented by a system of linear equations. A linear equation is an algebraic equation whose variable quantity or quantities are in the first power only and whose graph is a straight line. 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.
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