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4-LP-part2 - QMT437 Operations Research Pn Paezah Topic 3...

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QMT437 Operations Research Pn. Pa’ezah Topic 3: Linear Programming– Part 2 Outline Solving LP Problems by the Graphical Method Isoprofit/Isocost Method Corner Point Method Learning Outcomes At the end of the class, you will learn how to solve LP problems in two decision variables by graphing Graphical Solution (for LP problems in 2 variables) LP problems in two variables can be solved by the graphical method. The graphical procedure includes two main steps: Step 1: Determination of the feasible region. - Prepare a graph of the feasible solutions for each of the LP model constraints. The solution set of the system is that region (or set of ordered pairs), which satisfies ALL the constraints. This region is called the area of feasible solution or feasible region. Step 2: Determination of the optimum solution from all feasible points in the solution space using one the following methods: Method A: Isoprofit /Isocost Line Method ( isoprofit line method for maximization problems, or isocost line method for minimization problems) Method B: Corner (extreme) point method Method A: Isoprofit/isocost line method Draw objective function lines . Determine the optimum point . For maximization problems: Move parallel objective function lines toward larger objective function values without entirely leaving the feasible region. For minimization problems: Move parallel objective function lines toward smaller objective function values without entirely leaving the feasible region. The last feasible point touched by the objective function line before it leaves the feasible region is the optimum point.
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