Graphical Method Of Solving Linear Programming Problems

Graphical Method Of Solving Linear Programming Problems-31
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.He has Rs 50,000 to invest and has storage space of at most 60 pieces. He estimates that from the sale of one table, he can make a profit of Rs 250 and from the sale of one chair a profit of Rs 75.

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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.

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).

These situations and restrictions are known as the constraints of flying planes on the most popular and profitable route.

Linear programming is used to find the solution for the given constrained problem.You can calculate values of by putting another variable value to zero. Again, go to Select Data by right-clicking on the chart and add another series.Like for C1, at X = 0, Y’s value would be Y = 100 and at Y = 0, X’s value would be X = 20. Name it C2 and in X values select constraints C2 X column values and in Y values select constraints C2 Y column values.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.Your chart will look like the one below: Now you have 4 points (O, A, B, C) at feasible region area, you need to calculate objective function values at all the points to see which point gives you the maximum value of the objective.Step-6: To calculate objective function values, Follow the below steps: Calculate the objective function for each value of point: As you can see here in this linear maximization problem, you have got Z’s maximum value at Point B, and the maximum value is Rs. Hence, in order to maximize profit, the dealer must purchase 10 tables and 50 chairs.Successive constructed tableaux in the Simplex method will provide the value of the objective function at the vertices of the feasible region, adjusting simultaneously, the coefficients of initial and slack variables.In the initial tableau the value of the objective function at the O-vertex is calculated, the coordinates (0,0) correspond to the value which have the basic variables, being the result 0.A majority of airlines optimize flight schedules to get the highest revenue and lowest cost.These airlines schedules involve a lot of situations and restrictions such as the number of planes at a particular location, fuel, crew, and type of route (popular and profitable routes).


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