Graphical RepresentationLinear programming
- 2. The graphical method of solving a linear programming problem can be used when there are only two decision variables. If the problem has three or more variables, the graphical method is not suitable. In that case we use the SIMPLEX METHOD which will be discussed separately by our fellow classmate .
- 3. Let’s understand some important definitions and concepts before moving on with the Graphical Method: 1. Solution: A set of decision variables values which satisfy all the constraints of an LPP. 2. Feasible solution: Any solution which also satisfies the non-negativity limitations of the problem.
- 4. 3. Optimal feasible solution: Any feasible solution which maximizes or minimizes the objective function. 4. Feasible Region: The common region determined by all the constraints and non-negativity limitations of an LPP. 5. Corner point: A point in the feasible region that is the intersection of two boundary lines
- 5. Procedure • Step 1: Convert each inequality as equation • Step 2: Plot each equation on the graph • Step 3: Shade the ‘ Feasible Region’. Highlight the common Feasible region. Feasible Region :Set of all possible solutions. • Step 4 : Compute the coordinates of the corner points (of the feasible region). These corner points will represent the ‘Feasible Solution’. Feasible Solution: If it satisfies all the constraints and non negativity restrictions.
- 6. Procedure( Cont..) • Step 5 : Substitute the coordinates of the corner points into the objective function to see which gives the Optimal Value. That will be the ‘Optimal Solution’. Optimal Solution : If it optimizes (maximizes or minimizes) the objective function. Unbounded Solution : If the value of the objective function can be increased or decreased indefinitely, Such solutions are called Unbounded solution. Inconsistent Solution : It means the solution of problem does not exist. This is possible when there is no common feasible region.
- 18. The graphical method is one of the easiest way to solve a small LP problem. However this is useful only when the decision variables are not more than two. It is not possible to plot the solution on a two- dimensional graph when there are more than two variables and we must turn to more complex methods. Another limitation of graphical method is that, an incorrect or inconsistent graph will produce inaccurate answers, so one need to be very careful while drawing and plotting the graph. A very useful method of solving linear programming problems of any size is the so called Simplex method. Limitation of Graphical Method
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