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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
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 is the

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1.3_Linear_Programming_-_Computer_Solution_and_Sensitivity_Analysis

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