How To Solve Linear Programming Problems Graphically

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The process goes on through the HG-edge up to G-vertex, obtained data are shown in tableau IV.

At this point, the process ends, being able to check that the solution does not improve moving along GC-edge up to C-vertex (the current value of the Z-function is not increased).

This step occurs in the second iteration of the Simplex method, as shown in tableau II.

The corresponding value to F-vertex is calculated in it, and Z = 24 is the obtained value for the function.

Be it trying to find optimum distribution of funds to maximize country’s economy or trying to find best blend of materials to lower a building’s cost but maximize its life.

As the problem gets complex, it makes sense to move from a manual to more say, efficient and automated, mode of solution hunting process.

And do you always want to plot and solve these kinds of problems? Python has a nice package named Pu LP which can be used to solve optimization problems using Linear programming.

To start with we have to model the functions as variables and call Pu LP’s solver module to find optimum values.

The maximum value of the objective function is 33, and it corresponds to the values x = 3 and y = 12 (G-vertex coordinates).

In Graphical method is necessary to calculate the value of the objective function at each vertex of feasible region, while the Simplex method ends when the optimum value is found.


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