Solving Linear Programming Problems

Solving Linear Programming Problems-66
The graph must be constructed in ‘n’ dimensions, where ‘n’ is the number of decision variables.

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Choose the constant value in the equation of the objective function randomly, just to make it clearly distinguishable.

An optimum point always lies on one of the corners of the feasible region. Place a ruler on the graph sheet, parallel to the objective function.

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.

It could be viewed as the intersection of the valid regions of each constraint line as well.

Choosing any point in this area would result in a valid solution for our objective function.

It will clearly be a straight line since we are dealing with linear equations here.

One must be sure to draw it differently from the constraint lines to avoid confusion.

Here we are going to concentrate on one of the most basic methods to handle a linear programming problem i.e. In principle, this method works for almost all different types of problems but gets more and more difficult to solve when the number of decision variables and the constraints increases. We will first discuss the steps of the algorithm: We have already understood the mathematical formulation of an LP problem in a previous section.

Therefore, we’ll illustrate it in a simple case i.e. Note that this is the most crucial step as all the subsequent steps depend on our analysis here.

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