Linear programming graphical method maximization problem pdf

GRAPHICALMETHOD Step 1. Formulate the LP problem. Table 1 will help us formulate the problem. The bottom row is used to formulate the objective function. Objective functions are developed in such a way as to be either maximized or minimized. In this case, the company's management wishes to maximize unit profit. How to solve LinearProgramming problems? §geometric approach §simplex method approach Geometric Approach Step 1. Form a mathematical model for the problem. (a) Introduce decision variables and write a linear objective function. (b) Write problem constraints in the form of linear inequalities. (c) Write nonnegative constraints. Step 2. This is done by arranging the lines corresponding to the slope of the equation. Follow the following steps for the Iso-cost method solution: Step 1: Create a statistical design from a given problem. If not provided. Step 2: Now plan the graph using the given obstacles and find a region that you can use. Simple Linear Programming Problems13 1. Modeling Assumptions in Linear Programming14 2. Graphically Solving Linear Programs Problems with Two Variables (Bounded Case)16 3. Formalizing The Graphical Method17 4. Problems with Alternative Optimal Solutions18 5. Problems with No Solution20 6. Problems with Unbounded Feasible Regions22 Chapter 3. A non-graphical method of solution, called the Simplex Method, was developed by George Dantzig to solve these large problems. In this class, we'll look at the Simplex Method applied to special linear programming problems called standard maximization problems. Standard Maximization Problem: Maximize: P c x c x c x 1 1 2 2 nn, where c 12, n auxiliary problem has a feasible solution with XQ = 0 or, in other words, the original problem has a feasible solution if and only if the optimal value of the auxiliary problem is zero. The original problem is now solved using the simplex method, as described in the previous sections. This solution is called Phase 2. Rajib Bhattacharjya, IITG CE 602: Optimization Method Linear programming It is an optimization method applicable for the solution of optimization problem where objective function and the constraints are linear It was first applied in 1930 by economist, mainly in solving resource allocation problem Using the Simplex Method to Solve Linear Programming Maximization Problems J. Reeb and S. Leavengood EM 8720-E October 1998 $3.00 A key problem faced by managers is how to allocate scarce resources among activities or projects. Linear programming, or LP, is a method of allocating resources in an optimal way. It is one of the most widely used A graphical method for solving linear programming problems is outlined below. Solving Linear Programming Problems - The Graphical Method 1. Graph the system of constraints. This will give the feasible set. 2. Find each vertex (corner point) of the feasible set. 3. Substitute each vertex into the objective function to determine which vertex • graphical methods provide visualization of how a solution for a linear programming problem is obtained. 8 f graphical solution of a maximization model coordinate axes maximize z=$40x1 + 50x2 subject to 1x1 + 2x2 40 hours of labor 4x2 + 3x2 120 pounds of clay x1, x 2 0 coordinates for graphical analysis 9 f graphical … Linear Programming I: Maximization was published by on 2015-07-24. Find