3-1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Linear Programming: Computer Solution and Sensitivity Analysis Chapter 3-Part1

3-2 Beaver Creek Pottery Example Excel Spreadsheet – Data Screen (1 of 6) Exhibit 3.1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3-3 Beaver Creek Pottery Example “Solver” Parameter Screen (2 of 6) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 3.2

3-4 Exhibit 3.3 Beaver Creek Pottery Example Adding Model Constraints (3 of 6) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3-5 Beaver Creek Pottery Example “Solver” Settings (4 of 6) Exhibit 3.4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3-6 Exhibit 3.5 Beaver Creek Pottery Example Solution Screen (5 of 6) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3-7 Beaver Creek Pottery Example Answer Report (6 of 6) Exhibit 3.6 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3-8 Linear Programming Problem: Standard Form Standard form requires all variables in the constraint equations to appear on the left of the inequality (or equality) and all numeric values to be on the right-hand side. Examples:  x 3  x 1 + x 2 must be converted to x 3 - x 1 - x 2  0  x 1 /(x 2 + x 3 )  2 becomes x 1  2 (x 2 + x 3 ) and then x 1 - 2x 2 - 2x 3  0 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3-9 Sensitivity analysis determines the effect on the optimal solution of changes in parameter values of the objective function and constraint equations. Changes may be reactions to anticipated uncertainties in the parameters or to new or changed information concerning the model. Beaver Creek Pottery Example Sensitivity Analysis (1 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3-10 Maximize Z = $40x 1 + $50x 2 subject to: x 1 + 2x 2  40 4x 1 + 3x 2  120 x 1, x 2  0 Figure 3.1 Optimal Solution Point Beaver Creek Pottery Example Sensitivity Analysis (2 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3-11 Maximize Z = $100x 1 + $50x 2 subject to: x 1 + 2x 2  40 4x 1 + 3x 2  120 x 1, x 2  0 Figure 3.2 Changing the x 1 Objective Function Coefficient Beaver Creek Pottery Example Change x 1 Objective Function Coefficient (3 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3-12 Maximize Z = $40x 1 + $100x 2 subject to: x 1 + 2x 2  40 4x 1 + 3x 2  120 x 1, x 2  0 Figure 3.3 Changing the x 2 Objective Function Coefficient Beaver Creek Pottery Example Change x 2 Objective Function Coefficient (4 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall