Graphical Method Of Solving Linear Programming Problems

Graphical Method Of Solving Linear Programming Problems-52
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.

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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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.

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.

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.

The input base variable in the Simplex method determines towards what new vertex is performed the displacement.

In this example, as P1 (corresponding to 'x') enters, the displacement is carried out by the OF-edge to reach the F-vertex, where the Z-function value is calculated.

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.

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