SOLUTION OF LINEAR PROGRAMMING PROBLEMS: Solution of LPP: Using Simultaneous Equations and Graphical Method; Definitions: Feasible Solution, Basic and non-basic Variables, Basic Feasible Solution, Degenerate and Non-degenerate Solution, slack, surplus and artificial variable. An LP is degenerate if in a basic feasible solution, one of the basic variables takes on a zero value. ... Graphical method, simplex method, and transportation method are concerned with. a. degenerate solution. A linear programming problem is said to have unbounded solution if its solution can be made infinitely large without violating any of its constraints in the problem. Customers arrive at a box office window, being manned ny single individual, according to Poisson input process with mean rate of 20 per hour, while the mean service time is 2 minutes. Special Cases in Simplex Method Divyansh Verma SAU/AM(M)/2014/14 South Asian University Email : itsmedv91@gmail.com 4/18/2015 1 2. 5 .The graphical method can be used when an LPP has _____ decision variables. A basic feasible solution is called . one must use the northwest-corner method; Q93 – The purpose of the stepping-stone method is to. B. infeasible. [ 5L] Solution of LPP by Simplex Method; Charnes Big-M Method; Duality Theory. ... Purposeof MODI method is to get_____. 4-3 2 . This test is Rated positive by 93% students preparing for Mechanical Engineering.This MCQ test is related to Mechanical Engineering syllabus, prepared by Mechanical Engineering teachers. It cannot be determined in a graphical solution of an LPP. and using Big M method objective function becomes . 5.In Transportation problem optimal solution can be ... deterministic in nature. 1. A. c. It implies that there must be a convex region satisfying all the constraints. In LPP the condition to be satisfied is. M Method. Note that this solution can be obtained by solving a system of equations with the constraints 1 and 3 (R1 and R3) in equality. 1] When one or more of basic variables has ZERO value. d. Extreme points of the convex region gives the optimum solution. a. Infeasible region b. Unbounded region c. Infinite region d. 0 -4 . In graphical method of linear programming problem if the ios - cost line coincide with a side o f region of basic feasible solutions we get A. This situation is called degeneracy. x. 0 . Quantity value for a Basic variable is equal to zero in the simplex table. 0 . Solution: QUESTION: 3. b. polynomial method. How can I determine if a solution in a linear programming problem is degenerate without I use any software or the graphical display of the solution; For example in the model: $$\max\{2x_1 + 4x_2\}\\\phantom{ aa}\\ \text{s.t. Statement and formulation of L.P.P. Corner point method - definition The optimal solution to a LPP, if it exists, occurs at the corners of the feasible region. Max Z = 5x 1 – 2×2 + 3x 3 + OS 1 + OS 2 + OS 3 – Ma 1. (a) Infeasible region (b) Unbounded region (c) Infinite region (d) Feasible region (2) When it is not possible to find solution in LPP, it is called as case of _____. 3. Similarly, it is asked, what are basis variables? Give a two-dimensional graphical demonstration of the type of solu-tion space and objective function that will produce this result. Unbounded solution The solutions of a linear programming problem which is feasible can be classified as a bounded solution and an unbounded solution. x1 +x2 • 1 ¡x2 +x3 • 0 x1;x2;x3 ‚ 0 Which kind of limits are you referring to? The graphical method is applicable to solve the LPP involving two decision variables x 1, and x 2, we usually take these decision variables as x, y instead of x 1, x 2. (b) Transportation Problem- Statement of T. P., Feasible, basic feasible solution, degenerate solution, non-degenerate solution and optimal solution. Meaning of Degeneracy and Infeasibility in LPP. (You may use TORA for convenience.) of basic variables becomes less than equality constraint. In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has a vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph's edges. The unbounded solution is a situation when the optimum feasible solution cannot be determined, instead there are infinite many solutions. d. quadratic method . Solution by graphical method (for two variables), Convex set, hyperplane, extreme points, convex polyhedron, basic solutions and basic feasible solutions (b.f.s.). Otherwise the method results into cases where either no solution exists, or more than one solutions exist or the solutions are degenerative. It is independent of the objective function. x. Solution: Introducing the surplus variable S ≥ 0 slack variables S 2 ≥ 0, S 3 ≥ 0, and an artificial variable a 1 ≥ 0 the constraints of the problems becomes. B. a degenerate solution. Learning outcome 1.Finding the graphical solution to the linear programming model Graphical Method of solving Linear Programming Problems Introduction Dear students, during the preceding lectures, we have learnt how to formulate a given problem as a Linear Programming model. d. Quadratic equation. d. none of these. d. non-degenerate solution. In graphical method the restriction on number of constraint is _____. In an LPP if one of the decision variable is zero then the solution is. A variable is a basic variable if it corresponds to a pivot column. a. corner point solution method. Question 1: Operations… Read More » An unbounded solution of a linear programming problem is a situation where objective function is infinite. 0 . Degenerate and non-degenerate b.f.s.. Graphical Method in LPP This is a special case of Graphical Method in LPP. 61. b. Mention a method of finding a solution to an LPP with two variables. 6.Which method is used to get optimal solution in graphical method of solving an LPP? The set of all feasible solutions of an L.P.P.is a convex set. (1) The region of feasible solution in LPP graphical method is called ____. A feasible solution of LPP SOLUTION OF LINEAR PROGRAMMING PROBLEMS: Solution of LPP: Using Simultaneous Equations and Graphical Method; Definitions: Feasible Solution, Basic and non-basic Variables, Basic Feasible Solution, Degenerate and Non-degenerate Solution, slack, surplus and artificial variable. The corner point method includes the following steps Step 1: Find the feasible region of the LPP. Non-degenerate: A basic feasible solution is called non-degenerate if all m basic variables are non-zero and positive. In an LPP define (i) Solution (ii) Feasible solution (iii) Optimal solution (iv)Objective function (v) Decision variables (vi) Unbounded solution (vii) Multiple solution… c. modi method. For instance, consider the system of linear equations. 2 . BIG. Degeneracy is caused by redundant constraint(s) and could cost simplex method extra iterations, as demonstrated in the following example. Therefore w1 = 10/3, w2 = 0, and w3 = 5/3 gives an optimal solution to the dual problem. Contents • Simplex Method • Simplex Table • Special Cases of Simplex Method – Degeneracy – Alternative Optima – Unbounded Solution – Infeasible Solution • References 4/18/2015 2 3. 3. I see several different categories to consider. When applying the Simplex Method to calculate the minimum coefficient or feasibility condition, if there is a tie for the minimum ratio or minimum coefficient it can be broken arbitrarily. the solution must be optimal. In this course, the educator discusses the following topics LPP and inequation and their graph, formulation of LPP graphical solution, simplex method, big my and two-phase, duality and dual simplex method with examples. x. max z = x1 +x2 +x3 s.t. All faces are shown in bold.62 4.10 Visualization of the set D: This set really consists of the set of points on the red line. Home; Operations Research; Page 7; Operations Research. Big M method is a modified form of simplex method, and it is always used whenever the constraints are of (≥ or =) type irrespective of … D. a multiple number of optimal solutions. C. an unbound solution. Unbounded Solution c. degenerate solution. 0 1 = = 2 6 . Solution C. basic solution B. feasible solution D. optimal Graphical optimal value for Z can be obtained from A. Consider the following LPP : Max Z = 15x 1 + 10x 2 Subject to the constraints 4x 1 + 6x 2 ≤ 360 3x 1 + 0x 2 ≤ 180 0x 1 + 5x 2 ≤ 200 x 1, x 2 / 0 The solution of the LPP using Graphical solution technique is : Which of the following considers difference between two least costs for each row and column while finding initial basic feasible solution in transportation problem. Unit 2 2.1 Introduction to Linear Programming 2.2 General Form of LPP 2.3 Assumptions in LPP 2.4 Applications of Linear Programming 2.5 Advantages of Linear Programming Techniques 2.6 Formulation of … The optimal solution of the linear model is reached in the vertex C where X=100 and Y=350 with optimal value V(P)=3.100. LPP problem if the solution is feasible. (a) north west corner (b) least cost (c) Row minima method (d) Vogel’s approximation method 65. However, the solver tool can quickly solve an LPP problem. Step 2: Find the co-ordinates of each vertex of the feasible region. (a) Linear Programming Problem: Definition of LPP, Statement of its general form, Formulation of LPP with two variables and graphical solution-Feasible, Optimal, Multiple, Unbounded solutions. Simplex is a lengthy process. the solution is not degenerate. 2 b. Corner points of feasible region C. Botha and c B. corner points of the solution region D. none of the above In LPP the condition to be satisfied is A Constraints have to be linear C. both (a land [b] B. assist one in moving from an initial feasible solution to the optimal solution. develop the initial solution to the transportation problem. In the usual manner, the starting simplex table is obtained as below: Math 354 Summer 2004 Similarly, the first inequality in the dual problem can’t have slack, so substituting w1 = 10/3 and w2 = 0, we see that 10 3 +w3 = 5, so w3 = 5/3. Consequently the vertex C besides being a basic solution is an optimal basic solution. Lesson 3: Graphical method for solving LPP. Here, I have shown Basic solution connection with corner points in Graphical Solution of LPP. Optimum Basic Feasible Solution A basic feasible solution which optimizes (maximizes or minimizes) the objective function of the given LP model is called an optimum feasible solution to the given LPP. Hence, for one incoming variable, there are two outgoing variables. For the following LP, show that the optimal solution is degenerate and that none of the alternative solutions are corner points (you may use TORA for convenience). b. the restriction put on resources. 1 . The concept of obtaining a degenerate basic feasible solution in a LPP is known as degeneracy. (a) Unknown solution (b) Unbounded solution (c) Infeasible solution (d) Improper solution a. cost function. The degeneracy in a LPP may arise Lecture 8 Linear programming : Special cases in Simplex Metho At the initial stage when at least one basic variable is zero in the initial basic feasible solution. This tool can be used to enhance operations, improve efficiencies and really add value to academic research and teaching exercises.” – Peter Murray This chapter presents graphical solution method for solving any LP problem with only two decision variables. a) The determination of the solution space that defines the feasible solution.

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