If the goal is to maximize the objective function, find the point of contact of the ruler with the feasible region, which is the farthest from the origin. This is the optimum point for minimizing the function. If the goal is to minimize the objective function, find the point of contact of the ruler with the feasible region, which is the closest to the origin. Now begin from the far corner of the graph and tend to slide it towards the origin. We only need the direction of the straight line of the objective function. Be sure to keep the orientation of this ruler fixed in space. How to find it? Place a ruler on the graph sheet, parallel to the objective function. Step 6: Find the optimum point Optimum PointsĪn optimum point always lies on one of the corners of the feasible region. Choose the constant value in the equation of the objective function randomly, just to make it clearly distinguishable. One must be sure to draw it differently from the constraint lines to avoid confusion. It will clearly be a straight line since we are dealing with linear equations here. Step 5: Plot the objective function on the graph Choosing any point in this area would result in a valid solution for our objective function. It could be viewed as the intersection of the valid regions of each constraint line as well. The feasible solution region on the graph is the one which is satisfied by all the constraints. Step 4: Identify the feasible solution region If yes, then the side of the constraint lines on which the origin lies is the valid side. How to check? A simple method is to put the coordinates of the origin (0,0) in the problem and determine whether the objective function takes on a physical solution or not. This is used to determine the domain of the available space, which can result in a feasible solution. Step 3: Determine the valid side of each constraint line One must know that one cannot imagine more than 3-dimensions anyway! The constraint lines can be constructed by joining the horizontal and vertical intercepts found from each constraint equation. 
This should give you an idea about the complexity of this step if the number of decision variables increases. The graph must be constructed in ‘n’ dimensions, where ‘n’ is the number of decision variables.
Step 2: Construct a graph and plot the constraint lines
Linear Programming Problem and Its Mathematical Formulation. Different Types of Linear Programming Problems. Browse more Topics under Linear Programming Note that this is the most crucial step as all the subsequent steps depend on our analysis here. We have already understood the mathematical formulation of an LP problem in a previous section. We will first discuss the steps of the algorithm: Step 1: Formulate the LP (Linear programming) problem
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