Concepts of Linear Optimization with Application

Linear programming problem (LPP) is a mathematical method of determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear equations. LPP can be applied to various fields of study. It is used most extensively in business and economics but can also be utilized for some engineering problems. Industries that use LPP models include transportation, energy, telecommunications, and manufacturing. LPP can be solved by a graphical or simplex method. In graphical method, extreme points of the feasible solution space are examined to search for optimal solution at one of them. For a LPPs with several variables, we may not be able to graph the feasible region, but the optimal solution will still lie at an extreme point of the many sided figure that represents the area of feasible solutions. Since the number of extreme points (corners or vertices) of feasible solution space is finite, the method assures an improvement in the value of the objective function as we move from one iteration to another and achieve optimal solution in a finite number of steps.