Graphical Method Of Solving Linear Programming Problems

Graphical Method Of Solving Linear Programming Problems-20
You have covered a lot of details about linear programming.You learned what linear programming is, basic concepts, and terminologies used in LP, LP-problem formulation, solving LP problems using the graphical method, and use cases of the LP problem.The maximum value of the objective function is 33, and it corresponds to the values x = 3 and y = 12 (G-vertex coordinates).

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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.

LP is applicable in all kinds of problems such as economic activities in agriculture, engineering, manufacturing, energy, logistics, and supply chain.

Congratulations, you have made it to the end of this tutorial!

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 wants to know how many tables and chairs he should buy from the available money to maximize his total profit, assuming that he can sell all the items which he buys.Linear programming is applied to find optimal solutions for operations research.LP can find the most optimum solution in given constraints and restrictions.Hopefully, you can now utilize the linear programming concepts to make decisions in your organization or optimize your results for decision makers. Example: Isolating your constraints for $x_2$ yields: $$\begin 4x_1 5x_2 \le 2000 \quad\Rightarrow\quad x_2 \leq 400 - \frac \ 2.5x_1 7x_2 \le 1750 \quad\Rightarrow\quad x_2 \leq 250 - \frac \ 5x_1 4x_2 \le 2200 \quad\Rightarrow\quad x_2 \leq 550 - \frac \end$$ Plotting these yields; Where the area below the graph, but with $x_1, x_2 0$ is the solution space.LP problems can be solved using different techniques such as Graphical, Simplex, and Karmakar's method.Let's see the basic terminologies of linear programming: In a linear programming problem, the decision variables, objective function, and constraints all have to be a linear function Problem Statement: A furniture dealer deals in only two items–tables and chairs.As a manager of a company, you always have finite or limited resources, and top management's expectation is for you to make the most out of it.From time productivity to capital utilization, land to labor, and from supply chain to production-almost everything you do is to optimize productivity.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.


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