Linear Programming

Linear programming is abbreviated as LPP is a mathematical process of linear optimization. Linear Programming Definition says that it is used to determine maximum profit or minimum cost or minimum profit or maximum cost out of list of different Linear Equations or relationships. It is used for optimization of different linear terms. It may be linear inequality or linear equality which are represented in the form of graph and then according to linear equations it is determined. A cost is given for every Set of Linear Inequalities. After finding the optimized values for a particular region including all set of linear inequalities, these optimum values are substituted in cost equation which is to be optimized, and thus points at which we obtain most suitable optimum result is said to be the solution or we can say the optimized solution for that set of equations.

Now let us consider an example assuming 'Z' as cost of set of equations or inequalities. And there are three inequalities constituting in set of linear equations. Firstly we will find out the satisfiable values of 'x' and 'y' for each equation and create a graph which involves all three equations as part of it. These three equations form a common region or may be uncommon region which satisfies the cost for a set of inequalities. This region if it is common then optimized maximum profit is and if regions are not common then the cost found will be minimum. Consider the following graph, in this way we have a set of two inequalities say:
x + y < 2 and x = 2. One is an inequality and other one is an equation. The region thus obtained considering these two lines and cost is as follows: