# Graphical Sensitivity Analysis

May 5th, 2015
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Sensitivity Analysis Source: Introduction to Management Science 10 e, Anderson Sweeney Williams

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Graphical Sensitivity AnalysisSensitivity AnalysisSource: Introduction to Management Science 10 e, Anderson Sweeney WilliamsExample 1Max s.t. 5x1 + 7x2 x1 < 6 2x1 + 3x2 < 19 x1 + x2 < 8 x1, x2 > 0x28 7 6 5 4 3 2 1x1 + x2 < 8Max 5x1 + 7x2 x1 < 6 Optimal: x1 = 5, x2 = 3, z = 46 2x1 + 3x2 < 19 x112345678910x28 7 6 5 4 3 2 15 5Feasible Region1 11 2 3 44 4 3 3 2 25 6 7 8 9 10x1Example 1 Range of Optimality for c1 The slope of the objective function line is -c1/c2. The slope of the first binding constraint, x1 + x2 = 8, is -1 and the slope of the second binding constraint, x1 + 3x2 = 19, is -2/3. Find the range of values for c1 (with c2 staying 7) such that the objective function line slope lies between that of the two binding constraints: -1 < -c1/7 < -2/3 Multiplying through by -7 (and reversing the inequalities): 14/3 < c1 < 7Example 1 Range of Optimality for c2 Find the range of values for c2 ( with c1 staying 5) such that the objective function line slope lies between that of the two binding constraints: -1 < -5/c2 < -2/3 Multiplying by -1: Inverting, Multiplying by 5: 1 > 5/c2 > 2/3 1 < 5 < c2/5 < 3/2 c2 < 15/2Right-Hand Sides The improvement in the value of the optimal solution per unit increase in the right-hand side is called the dual price. The range of feasibility is the range over which the dual price is applicable. As the RHS increases, other constraints will become binding and limit the

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