1.3_Linear_Programming_-_Computer_Solution_and_Sensitivity_Analysis

1.3_Linear_Programming_-_Computer_Solution_and_Sensitivity_Analysis

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1 Linear Programming Part III: Computer Solution and Sensitivity Analysis Chapter 3 2 Chapter Outline ± To use computer package (LINDO) to solve LP problems ± To learn sensitivity analysis in LP 3 ± Recall some basic concepts in graphical solution method ± The optimal solution is one of the vertices (corner point) of the feasible region. ± The values of the variables at the corner points may be found by solving the corresponding set of the constraint equations. (Algebraic Solution) ± Searching optimal solution from one corner point to another corner point! ± Simplex method. Computer Solution to LP Problems 4 ± LINDO Package ± Ease of use. ± Trial version available for free download ( http://www.lindo.com/ => Downloads => Download Classic LINDO) Computer Package - LINDO Click here and follow instructions to download
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5 ± Solve a product-mix problem by LINDO package maximize Z = 40 x 1 + 50 x 2 subject to 1 x 1 + 2 x 2 40 4 x 1 + 3 x 2 120 x 1 0 x 2 0 Demonstration of Computer Solution to LP Problem 6 The maximum value of the objective function is 1360 . This occurs at X 1 = 24 and X 2 = 8 Computer Solution Output Objective function value at optimal points Optimal solution of decision variables 7 ± Sensitivity analysis (also refer to as “ what if analysis) is to investigate the impacts on optimal solution and objective function due to a change in a parameter: ± Change in Objective Function Coefficient ± Change in Constraint Right-Hand-Side Value (RHS) Sensitivity Analysis 8 ± Graphically, this change will only affect the slope of the objective function line but not the feasible region . ± May affect the optimality but not the feasibility . (i.e. may give a new optimal point.) Sensitivity Analysis – Change in Objective Function Coefficient
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9 Maximize Z = $40x 1 + $50x 2 subject to: 1x 1 + 2x 2 40 4x 1 + 3x 2 120 x 1 , x 2 0 Figure 3.1 Optimal Solution Point Beaver Creek Pottery Example (1 of 3) 10 Figure 3.2 Changing the x 1 Objective Function Coefficient Beaver Creek Pottery Example (2 of 3) Maximize Z = $ 100 x 1 + $50x 2 subject to: 1x 1 + 2x 2 40 4x 1 + 3x 2 120 x 1 , x 2 0 11 Beaver Creek Pottery Example (3 of 3) Figure 3.3 Changing the x 2 Objective Function Coefficient Maximize Z = $40x 1 + $ 100 x 2 subject to: 1x 1 + 2x 2 40 4x 1 + 3x 2 120 x 1 , x 2 0 12 ± The sensitivity range for an objective function coefficient
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This note was uploaded on 06/17/2010 for the course MS 3401 taught by Professor Sally during the Spring '10 term at City University of Hong Kong.

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1.3_Linear_Programming_-_Computer_Solution_and_Sensitivity_Analysis

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