What we did was, we found our the coordinates of the vertices of the feasible region, evaluated Z at each of these points and claimed with sufficient intuitive proof that the vertex that renders the best value for Z is indeed the optimum of the LP.
Hence, it only makes sense, to try and find the vertices of the feasible region in our algebraic method as well. Our knowledge of algebra allows us to solve equations and not inequalities to hopefully arrive at a singular point.
Hence if we have any hope of finding out the vertices of the feasible region with the tools of algebra, we must convert the inequalities that currently represent our constraints into equations.
It must be worthwhile to pause here and think about how one can do this instead of reading ahead to the solution.
Explains how linear programming (an operations research method for optimizing the allocation of resources) is a useful tool for managers planning single or multiple manufacturing facilities.
Thesis Statement For Causes Of Obesity - Use Graphical Methods To Solve The Linear Programming Problem
Includes step-by-step instructions on: (1) how to translate a real-world problem into the linear programming equations necessary to create a valid model and (2) how to use the model to determine the optimal solution to the real-world problem.
For the sake of convenience, I have restated the problem and the graph for the same below: The final graph of the solved LP is shown on the figure below.
As we found out earlier, point B is the optimum of this problem with a Z value of 180.
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In the last section we discussed the graphical method to solve almost any two variable linear programming problem.