linear programming Graph method

Linearity implies that the LP must satisfy three basic properties:Proportionality: this property requires the contribution of each decision variable in both the objective function and the constrain to be directly proportional to the value of the variable. Additivity: this property requires the total contribution of all the variables in the objective function and in the constraints to be the direct sum of the individual contributions of each variable. certainty: all the objective and constraint coefficients of the LP model are deterministic. This means that they are known constants- a rare occurrence in real life, where data are more likely to be represented by probabilistic distributions. In essence, LP coefficients are average- value approximations of the probabilistic distributions. If the standard deviation of these distributions are sufficiently small, then the approximation is acceptable. Large standard deviation can be accounted for directly by using stochastic LP algorithms or indirectly by applying sensitivity analysis to the optimum solution..The graphical procedure includes four steps: Step 1: Draw coordinate space Tradition is that x1 is the horizontal axis and x2 is the vertical axis. Because of the non-negativity constraints on x1 and x2 it is enough to draw the 1st quadrant. Step 2: Draw constraint-lines each constraint consists of a line and of information (e.g. arrows) indicating which side of the line is feasible. Step 3: Define feasible region This is done by selecting the region satisfied by all the constraints including the non-negativity constraints. Step 4: Find the optimum by moving the isoprofit line The isoprofit line is the line where the objective function is constant. The procedure uses two examples to show how maximization and minimization objective functions are handled.