We can see that the blue line ($x_2 \leq 400 - \frac$) is superfluous for defining the solution space, and thus leave it out.
Your maximization function isolated for $x_2$ yields: $$ 55x_1 500x_2 = 0 \\ \Downarrow \\ x_2 = -\frac $$ Adding this to the plot, yields the following graph (new blue line = maximization function): Now 'shoving' this maximization function line 'up' yields the following; At this point the line cannot be 'shoved' further 'up', without entirely leaving the solution space.
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.
The process goes on through the HG-edge up to G-vertex, obtained data are shown in tableau IV.
Graphical Method Of Solving Linear Programming Problems Communication Essay
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).
In this tutorial, you are going to learn about linear programming, and the following topics will be covered: Mathematically, linear programming optimizes (minimizes or maximizes) the linear objective of several variables subject to the given conditions/constraints that satisfies a set of linear inequalities.
Linear programming can be applied in planning economic activities such as transportation of goods and services, manufacturing products, optimizing the electric power systems, and network flows.
We all have finite resources and time and we want to make the most of them.
From using your time productively to solving supply chain problems for your company – everything uses optimization.